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Search: a259375 -id:a259375
Displaying 1-10 of 15 results found. page 1 2
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A259380 Palindromic numbers in bases 2 and 8 written in base 10. +10
17
0, 1, 3, 5, 7, 9, 27, 45, 63, 65, 73, 195, 219, 325, 341, 365, 381, 455, 471, 495, 511, 513, 585, 1539, 1755, 2565, 2709, 2925, 3069, 3591, 3735, 3951, 4095, 4097, 4161, 4617, 4681, 12291, 12483, 13851, 14043, 20485, 20613, 20805, 20933, 21525, 21653, 21845, 21973, 23085, 23213, 23405, 23533, 24125, 24253, 24445, 24573, 28679, 28807, 28999, 29127, 29719, 29847 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Index entries for sequences related to palindromes
FORMULA
Intersection of A006995 and A029803.
EXAMPLE
2709 is in the sequence because 2709_10 = 5225_8 = 101010010101_2.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 2], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=2; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 30000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
base,nonn
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259374 Palindromic numbers in bases 3 and 5 written in base 10. +10
16
0, 1, 2, 4, 26, 52, 1066, 1667, 2188, 32152, 67834, 423176, 437576, 14752936, 26513692, 27711772, 33274388, 320785556, 1065805109, 9012701786, 9256436186, 12814126552, 18814619428, 201241053056, 478999841578, 670919564984, 18432110906024, 158312796835916, 278737550525722 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
0 is only 0 regardless of the base,
1 is only 1 regardless of the base,
2 on the other hand is also 10 in base 2, denoted as 10_2,
3 is 3 in all bases greater than 3, but is 11_2 and 10_3.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..39
A.H.M. Smeets, Scatterplot of log_3(number is palindromic in base 3 and base b) versus b, for b in {2,4,5, 6,7,8,10}
FORMULA
Intersection of A014190 and A029952.
EXAMPLE
52 is in the sequence because 52_10 = 202_5 = 1221_3.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 5]; If[ palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=5; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 15 2015 *)
PROG
(Python)
def nextpal(n, b): # returns the palindromic successor of n in base b
....m, pl = n+1, 0
....while m > 0:
........m, pl = m//b, pl+1
....if n+1 == b**pl:
........pl = pl+1
....n = (n//(b**(pl//2))+1)//(b**(pl%2))
....m = n
....while n > 0:
........m, n = m*b+n%b, n//b
....return m
n, a3, a5 = 0, 0, 0
while n <= 20000:
....if a3 < a5:
........a3 = nextpal(a3, 3)
....elif a5 < a3:
........a5 = nextpal(a5, 5)
....else: # a3 == a5
........print(n, a3)
........a3, a5, n = nextpal(a3, 3), nextpal(a5, 5), n+1
# A.H.M. Smeets, Jun 03 2019
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380-A259384, A099145, A259385-A259390, A099146, A007632, A007633, A029961-A029964, A029804, A029965-A029970, A029731, A097855, A250408-A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 14 2015
STATUS
approved
A259376 Palindromic numbers in bases 4 and 6 written in base 10. +10
16
0, 1, 2, 3, 5, 21, 55, 215, 819, 1885, 7373, 7517, 12691, 14539, 69313, 196606, 1856845, 3314083, 5494725, 33348861, 223892055, 231755895, 322509617, 3614009815, 4036503055, 4165108015, 9233901154, 9330794722, 12982275395, 107074105033, 186398221946, 270747359295, 401478741365, 1809863435625, 2281658774290, 11931403417210, 12761538567790, 12887266632430, 15822654274715, 30255762326713, 46164680151002, 323292550693473, 329536806222753 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..64
FORMULA
Intersection of A014190 and A029953.
EXAMPLE
55 is in the sequence because 55_10 = 131_6 = 313_4.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 6]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 15 2015
STATUS
approved
A259377 Palindromic numbers in bases 3 and 7 written in base 10. +10
16
0, 1, 2, 4, 8, 16, 40, 100, 121, 142, 164, 242, 328, 400, 1312, 8200, 9103, 14762, 54008, 76024, 108016, 112048, 233920, 532900, 639721, 741586, 2585488, 3316520, 11502842, 24919360, 35664908, 87001616, 184827640, 4346524576, 5642510512, 11641189600, 65304259157, 68095147754, 469837033600, 830172165614, 17136683996456, 21772277941544, 22666883572232, 45221839119556 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..72
Index entries for sequences related to palindromes
FORMULA
Intersection of A014190 and A029954.
EXAMPLE
142 is in the sequence because 142_10 = 262_7 = 12021_3.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 7]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=7; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1] && d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A007632, A007633, A029731, A029804, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A048268, A060792, A097855, A097856, A097928, A097929, A097930, A097931, A099145, A099146, A099165, A182232, A182233, A182234, A250408, A250409, A250410, A250411, A250412, A259374, A259375, A259376, A259377, A259378, A249156, A259380, A259381, A259382, A259383, A259384, A259385, A259386, A259387, A259388, A259389, A259390.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259378 Palindromic numbers in bases 4 and 7 written in base 10. +10
16
0, 1, 2, 3, 5, 85, 150, 235, 257, 8802, 9958, 13655, 14811, 189806, 428585, 786435, 9262450, 31946605, 34179458, 387973685, 424623193, 430421657, 640680742, 742494286, 1692399385, 22182595205, 30592589645, 1103782149121, 1134972961921, 1871644872505, 2047644601565, 3205015384750, 3304611554563, 3628335729863, 4467627704385 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..48
Index entries for sequences related to palindromes
FORMULA
Intersection of A014192 and A029954.
EXAMPLE
85 is in the sequence because 85_10 = 151_7 = 1111_4.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 7]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=7; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259382 Palindromic numbers in bases 4 and 8 written in base 10. +10
16
0, 1, 2, 3, 5, 63, 65, 105, 130, 170, 195, 235, 325, 341, 357, 373, 4095, 4097, 4161, 4225, 4289, 6697, 6761, 6825, 6889, 8194, 8258, 8322, 8386, 10794, 10858, 10922, 10986, 12291, 12355, 12419, 12483, 14891, 14955, 15019, 15083, 20485, 20805, 21525, 21845 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Index entries for sequences related to palindromes
FORMULA
Intersection of A014192 and A029803.
EXAMPLE
235 is in the sequence because 235_10 = 353_8 = 3223_4.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 30000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
EXTENSIONS
Corrected and extended by Giovanni Resta, Jul 16 2015
STATUS
approved
A259384 Palindromic numbers in bases 6 and 8 written in base 10. +10
16
0, 1, 2, 3, 4, 5, 7, 154, 178, 203, 5001, 7409, 315721, 567434, 1032507, 46823602, 56939099, 84572293, 119204743, 1420737297, 1830945641, 2115191225, 3286138051, 3292861699, 4061216947, 8094406311, 43253138565, 80375377033, 88574916241, 108218625313, 116606986537, 116755331881, 166787896538, 186431605610, 318743407660, 396619220597, 1756866976011, 4920262093249, 11760498311914, 15804478291811, 15813860880803, 24722285628901, 33004205249575, 55584258482529, 371039856325905, 401205063672537, 516268720555889 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..74
Index entries for sequences related to palindromes
FORMULA
Intersection of A029953 and A029803.
EXAMPLE
178 is in the sequence because 178_10 = 262_8 = 454_6.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 6], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=6; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259385 Palindromic numbers in bases 2 and 9 written in base 10. +10
16
0, 1, 3, 5, 7, 127, 255, 273, 455, 6643, 17057, 19433, 19929, 42405, 1245161, 1405397, 1786971, 2122113, 3519339, 4210945, 67472641, 90352181, 133638015, 134978817, 271114881, 6080408749, 11022828069, 24523959661, 25636651261, 25726334461, 28829406059, 1030890430479, 1032991588623, 1085079274815, 1616662113341 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..44
A.H.M. Smeets, Scatterplot of log_2(number is palindromic in base 2 and base b) versus b, for b in {3,5,6,7,9,10}
Index entries for sequences related to palindromes
FORMULA
Intersection of A006995 and A029955.
EXAMPLE
273 is in the sequence because 273_10 = 333_9 = 100010001_2.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 2], AppendTo[lst, pp]; Print[pp]]; k++]; lst
PROG
(Python)
def nextpal(n, base): # m is the first palindrome successor of n in base base
m, pl = n+1, 0
while m > 0:
m, pl = m//base, pl+1
if n+1 == base**pl:
pl = pl+1
n = n//(base**(pl//2))+1
m, n = n, n//(base**(pl%2))
while n > 0:
m, n = m*base+n%base, n//base
return m
n, a2, a9 = 0, 0, 0
while n <= 30:
if a2 < a9:
a2 = nextpal(a2, 2)
elif a9 < a2:
a9 = nextpal(a9, 9)
else: # a2 == a9
print(a2, end=", ")
a2, a9, n = nextpal(a2, 2), nextpal(a9, 9), n+1 # A.H.M. Smeets, Jun 03 2019
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259386 Palindromic numbers in bases 3 and 9 written in base 10. +10
16
0, 1, 2, 4, 8, 10, 20, 40, 80, 82, 91, 100, 164, 173, 182, 328, 364, 400, 656, 692, 728, 730, 820, 910, 1460, 1550, 1640, 2920, 3280, 3640, 5840, 6200, 6560, 6562, 6643, 6724, 7300, 7381, 7462, 8038, 8119, 8200, 13124, 13205, 13286, 13862, 13943, 14024, 14600, 14681, 14762, 26248, 26572, 26896, 29200, 29524, 29848, 32152, 32476, 32800, 52496, 52820, 53144, 55448, 55772, 56096, 58400, 58724, 59048, 59050, 59860, 60670, 65620, 66430, 67240, 72190, 73000, 73810 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Index entries for sequences related to palindromes
FORMULA
Intersection of A014190 and A029955.
EXAMPLE
40 is in the sequence because 40_10 = 44_9 = 1111_3.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=9; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 80000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015
STATUS
approved
A259390 Palindromic numbers in bases 7 and 9 written in base 10. +10
16
0, 1, 2, 3, 4, 5, 6, 8, 40, 50, 100, 164, 200, 264, 300, 328, 400, 2000, 3550, 8200, 10252, 14510, 14762, 22800, 45600, 164900, 201720, 400200, 532900, 555013, 738100, 2756120, 2913368, 3344352, 3501600, 4084000, 12990350, 22674550, 194062432, 1684866370, 2225211080, 13575144288, 15127811455, 20404027400, 20537111057, 22668403353, 30862471355, 83714515310, 84668107250, 796259955485, 1202029647736, 2088800185930, 20268849562000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..86
Index entries for sequences related to palindromes
FORMULA
Intersection of A029954 and A029955.
EXAMPLE
264 is in the sequence because 264_10 = 323_9 = 525_7.
MATHEMATICA
(* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 7], AppendTo[lst, pp]; Print[pp]]; k++]; lst
CROSSREFS
Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
KEYWORD
nonn,base
AUTHOR
Eric A. Schmidt and Robert G. Wilson v, Jul 17 2015
STATUS
approved
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Last modified August 30 15:13 EDT 2024. Contains 375545 sequences. (Running on oeis4.)