Displaying 1-10 of 15 results found.
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
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,
Palindromic numbers in bases 3 and 6 written in base 10.
+10
16
0, 1, 2, 4, 28, 80, 160, 203, 560, 644, 910, 34216, 34972, 74647, 87763, 122420, 221068, 225064, 6731644, 6877120, 6927700, 7723642, 8128762, 8271430, 77894071, 78526951, 539212009, 28476193256, 200267707484, 200316968444, 201509576804, 201669082004, 231852949304, 232018753064, 232039258376, 333349186006, 2947903946317, 5816975658914, 5817003372578, 11610051837124, 27950430282103, 81041908142188
COMMENTS
Agrees with the number of minimal dominating sets of the halved cube graph Q_n/2 for at least n=1 to 5. - Eric W. Weisstein, Sep 06 2021
EXAMPLE
28 is in the sequence because 28_10 = 44_6 = 1001_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, 6]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst b1=3; b2=6; 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 *)
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.
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
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,
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
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.
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
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.
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
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.
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
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.
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
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.
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
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,
Palindromic numbers in bases 3 and 8 written in base 10.
+10
15
0, 1, 2, 4, 121, 130, 203, 316, 8578, 9490, 17492, 944035, 1141652, 1276916, 1554173, 58961443, 67470916, 4099065139, 5691134677, 81452592329, 81473867465, 419572845958, 21056462595764, 363376288168081
EXAMPLE
121 is in the sequence because 121_10 = 171_8 = 11111_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, 8]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst b1=3; 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,
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