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Search: a052216 -id:a052216
Displaying 11-20 of 54 results found.
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A052220
Numbers whose sum of digits is 6.
+10
34
6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600, 1005, 1014, 1023, 1032, 1041, 1050, 1104, 1113, 1122, 1131, 1140, 1203, 1212, 1221, 1230, 1302, 1311, 1320, 1401, 1410
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 6; number of repdigits = #{6,33,222,111111} = A242627(6) = 4. - Reinhard Zumkeller, Jul 17 2014
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..12376 (terms 1..924 from Vincenzo Librandi; all terms with <= 12 digits)
MATHEMATICA
Select[Range[10^4], Total[IntegerDigits[#]] == 6 &] (* Vincenzo Librandi, Mar 07 2013 *)
PROG
(Magma) [n: n in [1..1500] | &+Intseq(n) eq 6 ]; // Vincenzo Librandi, Mar 07 2013
(Haskell)
a052220 n = a052220_list !! (n-1)
a052220_list = filter ((== 6) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
(Python)
from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits):
alst = []
for d in range(1, maxdigits+1):
digset = "0"*(d-1) + "11111122233456"
for p in multiset_permutations(digset, d):
if p[0] != '0' and sum(map(int, p)) == 6:
alst.append(int("".join(p)))
return alst
print(auptodigs(4)) # Michael S. Branicky, Jun 15 2021
CROSSREFS
Cf. A007953.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Henry Bottomley, Feb 01 2000
EXTENSIONS
Offset changed from Bruno Berselli, Mar 07 2013
STATUS
approved
A166459
Numbers whose sum of digits is 19.
+10
34
199, 289, 298, 379, 388, 397, 469, 478, 487, 496, 559, 568, 577, 586, 595, 649, 658, 667, 676, 685, 694, 739, 748, 757, 766, 775, 784, 793, 829, 838, 847, 856, 865, 874, 883, 892, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1099, 1189, 1198, 1279, 1288
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 19; number of repdigits = A242627(19) = 1. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[1500], Total[IntegerDigits[#]]==19&] (* Harvey P. Dale, Jul 19 2011 *)
PROG
(Magma) [n: n in [1..1500] | &+Intseq(n) eq 19]; // Vincenzo Librandi, Sep 13 2013
(Haskell)
a166459 n = a166459_list !! (n-1)
a166459_list = filter ((== 19) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, Oct 14 2009
STATUS
approved
A143164
Numbers with digitsum 13, in increasing order.
+10
33
49, 58, 67, 76, 85, 94, 139, 148, 157, 166, 175, 184, 193, 229, 238, 247, 256, 265, 274, 283, 292, 319, 328, 337, 346, 355, 364, 373, 382, 391, 409, 418, 427, 436, 445, 454, 463, 472, 481, 490, 508, 517, 526, 535, 544, 553, 562, 571, 580, 607, 616, 625, 634, 643, 652
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If 13 is considered as an 'unlucky' number: the 'unlucky years'.
A007953(a(n)) = 13; number of repdigits = A242627(13) = 1. - Reinhard Zumkeller, Jul 17 2014
REFERENCES
The Guardian Weekly, July 25-31, 2008, p.39 puzzles 5., p31.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
Wolfdieter Lang, a(n) up to 3000
Eric Weisstein's World of Mathematics, Triskaidekaphobia
Wikipedia, Triskaidekaphobia
FORMULA
digitsum(a(n))=13, ordered increasingly.
EXAMPLE
2029 is the next 'unlucky year'. Solution to the guardian weekly puzzle.
a(10^ 1) = 166
a(10^ 2) = 1309
a(10^ 3) = 21370
a(10^ 4) = 1100254
a(10^ 5) = 111032122
a(10^ 6) = 30611101000
a(10^ 7) = 40100300100301
a(10^ 8) = 200011001012211010
a(10^ 9) = 10001220000100012002100
a(10^10) = 1100000001010021010000000230 - David A. Corneth, Jan 31 2015
MATHEMATICA
f[n_] := Rest@ Select[Range@ n, NestWhile[Plus @@ IntegerDigits[#] &, #, # > 14 &] == 13 &]; f@ 652 (* Michael De Vlieger, Feb 03 2015 *)
Select[Range[700], Total[IntegerDigits[#]]==13&] (* Harvey P. Dale, Oct 11 2017 *)
PROG
(Haskell)
a143164 n = a143164_list !! (n-1)
a143164_list = filter ((== 13) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
(PARI)
\\This algorithm needs a modified binomial.
C(n, k)=if(n>=k, binomial(n, k), 0)
\\ways to roll s-q with q dice having sides 0 through n - 1.
b(s, q, n)=if(s<=q*(n-1), s+=q; sum(i=0, q-1, (-1)^i*C(q, i)*C(s-1-n*i, q-1)), 0)
\\main algorithm
a(n) = {my(q); q = 2; while(b(13, q, 10) < n, q++); q--; s = 13; os = 13; r=0; while(q, if(b(s, q, 10) < n, n-=b(s, q, 10); s--, r+=(os-s)*10^(q); os = s; q--)); r+= s; r}
\\inverse
inv(n)={r = 1; v=digits(n); l=v[#v]; forstep(i = #v-1, 1, -1, for(j=1, v[i], r+=b(l+j, #v-i, 10)); l+=v[i]); r} \\ David A. Corneth, Jan 31 2015
(PARI) transform(n, b)=my(d=digits(n), nd=#d, v=vector(b, i, [i\10, b-(b+1-i)\10]), k); v[b][2]=d[1]; v
list(lim)=my(v=List(), d=transform(lim\=1, 13)); forvec(u=transform(lim\1, 13), if(u[4]<u[10] || (u[1]<u[10] && u[2]<u[11] && u[3]<u[12] && u[4]<u[13]), my(s=sum(i=1, 13, 10^u[i])); if(s<=lim, listput(v, s))), 1); Set(v) \\ Charles R Greathouse IV, May 30 2019
CROSSREFS
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Wolfdieter Lang, Sep 15 2008
STATUS
approved
A235151
Numbers whose sum of digits is 12.
+10
32
39, 48, 57, 66, 75, 84, 93, 129, 138, 147, 156, 165, 174, 183, 192, 219, 228, 237, 246, 255, 264, 273, 282, 291, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 408, 417, 426, 435, 444, 453, 462, 471, 480, 507, 516, 525, 534, 543, 552, 561, 570, 606
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 12; number of repdigits = #{66,444,3333,222222,1^12} = A242627(12) = 5. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[2000], Total[IntegerDigits[#]]==12&]
PROG
(Magma) [n: n in [1..1000] | &+Intseq(n) eq 12];
(Haskell)
a235151 n = a235151_list !! (n-1)
a235151_list = filter ((== 12) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
A242614, A242627.
KEYWORD
nonn,base
AUTHOR
Vincenzo Librandi, Jan 04 2014
STATUS
approved
A235227
Numbers whose sum of digits is 16.
+10
32
79, 88, 97, 169, 178, 187, 196, 259, 268, 277, 286, 295, 349, 358, 367, 376, 385, 394, 439, 448, 457, 466, 475, 484, 493, 529, 538, 547, 556, 565, 574, 583, 592, 619, 628, 637, 646, 655, 664, 673, 682, 691, 709, 718, 727, 736, 745, 754, 763, 772, 781, 790
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 16; number of repdigits = #{88,4444,22222222,1^16} = A242627(16) = 4. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[1000], Total[IntegerDigits[#]]==16 &]
PROG
(Magma) [n: n in [1..1000] | &+Intseq(n) eq 16];
(Haskell)
a235227 n = a235227_list !! (n-1)
a235227_list = filter ((== 16) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
base,nonn
AUTHOR
Vincenzo Librandi, Jan 05 2014
STATUS
approved
A235228
Numbers whose sum of digits is 18.
+10
32
99, 189, 198, 279, 288, 297, 369, 378, 387, 396, 459, 468, 477, 486, 495, 549, 558, 567, 576, 585, 594, 639, 648, 657, 666, 675, 684, 693, 729, 738, 747, 756, 765, 774, 783, 792, 819, 828, 837, 846, 855, 864, 873, 882, 891, 909, 918, 927, 936, 945, 954, 963
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 18; number of repdigits = #{99,666,333333,222222222,1^18} = A242627(18) = 5. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = 9*A279769(n). - M. F. Hasler, Dec 23 2016
MATHEMATICA
Select[Range[1000], Total[IntegerDigits[#]] == 18 &]
PROG
(Magma) [n: n in [1..1000] | &+Intseq(n) eq 18];
(Haskell)
a235228 n = a235228_list !! (n-1)
a235228_list = filter ((== 18) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A061423, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, Jan 05 2014
STATUS
approved
A166370
Numbers whose sum of digits is 17.
+10
31
89, 98, 179, 188, 197, 269, 278, 287, 296, 359, 368, 377, 386, 395, 449, 458, 467, 476, 485, 494, 539, 548, 557, 566, 575, 584, 593, 629, 638, 647, 656, 665, 674, 683, 692, 719, 728, 737, 746, 755, 764, 773, 782, 791, 809, 818, 827, 836, 845, 854, 863, 872
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 17; number of repdigits = A242627(17) = 1. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[900], Total[IntegerDigits[#]] == 17&] (* Vincenzo Librandi, Mar 07 2013 *)
PROG
(Magma) [n: n in [1..900] | &+Intseq(n) eq 17]; // Vincenzo Librandi, Mar 07 2013
(Haskell)
a166370 n = a166370_list !! (n-1)
a166370_list = filter ((== 17) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A011557, A052216 * A052224, A143164, A166311, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base
AUTHOR
Vincenzo Librandi, Oct 13 2009
STATUS
approved
A235225
Numbers whose sum of digits is 14.
+10
31
59, 68, 77, 86, 95, 149, 158, 167, 176, 185, 194, 239, 248, 257, 266, 275, 284, 293, 329, 338, 347, 356, 365, 374, 383, 392, 419, 428, 437, 446, 455, 464, 473, 482, 491, 509, 518, 527, 536, 545, 554, 563, 572, 581, 590, 608, 617, 626, 635, 644, 653, 662
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 14; number of repdigits = #{77,2222222,1^14} = A242627(14) = 3. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[1000], Total[IntegerDigits[#]] == 14 &]
PROG
(Magma) [n: n in [1..1000] | &+Intseq(n) eq 14];
(Haskell)
a235225 n = a235225_list !! (n-1)
a235225_list = filter ((== 14) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, Jan 05 2014
STATUS
approved
A235229
Numbers whose sum of digits is 20.
+10
31
299, 389, 398, 479, 488, 497, 569, 578, 587, 596, 659, 668, 677, 686, 695, 749, 758, 767, 776, 785, 794, 839, 848, 857, 866, 875, 884, 893, 929, 938, 947, 956, 965, 974, 983, 992, 1199, 1289, 1298, 1379, 1388, 1397, 1469, 1478, 1487, 1496, 1559, 1568, 1577, 1586
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 20; number of repdigits = #{5555,44444,2222222222,1^20} = A242627(20) = 4. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[2000], Total[IntegerDigits[#]]==20&]
PROG
(Magma) [n: n in [1..2000] | &+Intseq(n) eq 20];
(Haskell)
a235229 n = a235229_list !! (n-1)
a235229_list = filter ((== 20) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19).
Cf. A242614, A242627.
KEYWORD
base,nonn
AUTHOR
Vincenzo Librandi, Jan 05 2014
STATUS
approved
A235226
Numbers whose sum of digits is 15.
+10
30
69, 78, 87, 96, 159, 168, 177, 186, 195, 249, 258, 267, 276, 285, 294, 339, 348, 357, 366, 375, 384, 393, 429, 438, 447, 456, 465, 474, 483, 492, 519, 528, 537, 546, 555, 564, 573, 582, 591, 609, 618, 627, 636, 645, 654, 663, 672, 681, 690, 708, 717, 726, 735
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A007953(a(n)) = 15; number of repdigits = #{555,33333,1^15} = A242627(15) = 3. - Reinhard Zumkeller, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[1000], Total[IntegerDigits[#]] == 15 &]
PROG
(Magma) [n: n in [1..1000] | &+Intseq(n) eq 15];
(Haskell)
a235226 n = a235226_list !! (n-1)
a235226_list = filter ((== 15) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A052217 - A052224, A143164, A166311, A166370, A166459, A235227, A235229.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, Jan 05 2014
STATUS
approved
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