A052218 -id:A052218 - cp's OEIS frontend

A052220 Numbers whose sum of digits is 6.

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

Offset: 1

Henry Bottomley, Feb 01 2000

A007953(a(n)) = 6; number of repdigits = #{6,33,222,111111} = A242627(6) = 4. - Reinhard Zumkeller, Jul 17 2014

There are binomial(t + 4, 5) terms having exactly t digits. Therefore binomial(t + 5, 6) have at most t digits. - David A. Corneth, Jun 29 2025

			1023 is in the sequence as it has digital sum 1 + 0 + 2 + 3 = 6. - _David A. Corneth_, Jun 29 2025

Michael S. Branicky, Table of n, a(n) for n = 1..12376 (terms 1..924 from Vincenzo Librandi; all terms with <= 12 digits)

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.

a052220 n = a052220_list !! (n-1)
a052220_list = filter ((== 6) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1500] | &+Intseq(n) eq 6 ]; // Vincenzo Librandi, Mar 07 2013

Select[Range[10^4], Total[IntegerDigits[#]] == 6 &] (* Vincenzo Librandi, Mar 07 2013 *)

nxt(n) = {my(v, c, toadd); v = valuation(n, 10); c = (n / 10^v)%10; toadd = 10^(v)*(10 - c) + c - 1; return(n + toadd)} \\ David A. Corneth, Jun 29 2025

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

a(n) = a(n-1) + 10^v * (10 - c) + c-1 where c is the last nonzero digit of a(n) and v is the 10-adic valuation of a(n-1) and n > 1. - David A. Corneth, Jun 29 2025

Offset changed by Bruno Berselli, Mar 07 2013

A166459 Numbers whose sum of digits is 19.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Oct 14 2009

A007953(a(n)) = 19; number of repdigits = A242627(19) = 1. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a166459 n = a166459_list !! (n-1)
a166459_list = filter ((== 19) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1500] | &+Intseq(n) eq 19]; // Vincenzo Librandi, Sep 13 2013

Select[Range[1500],Total[IntegerDigits[#]]==19&] (* Harvey P. Dale, Jul 19 2011 *)

A143164 Numbers with digitsum 13, in increasing order.

Original entry on oeis.org

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

Offset: 1

Wolfdieter Lang, Sep 15 2008

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

			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

The Guardian Weekly, July 25-31, 2008, p.39 puzzles 5., p31.

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

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.

a143164 n = a143164_list !! (n-1)
a143164_list = filter ((== 13) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

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 *)

\\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

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]Charles R Greathouse IV, May 30 2019

digitsum(a(n))=13, ordered increasingly.

A235151 Numbers whose sum of digits is 12.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 04 2014

A007953(a(n)) = 12; number of repdigits = #{66,444,3333,222222,1^12} = A242627(12) = 5. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235151 n = a235151_list !! (n-1)
a235151_list = filter ((== 12) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 12];

Select[Range[2000], Total[IntegerDigits[#]]==12&]

A235227 Numbers whose sum of digits is 16.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 16; number of repdigits = #{88,4444,22222222,1^16} = A242627(16) = 4. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235227 n = a235227_list !! (n-1)
a235227_list = filter ((== 16) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 16];

Select[Range[1000], Total[IntegerDigits[#]]==16 &]

A235228 Numbers whose sum of digits is 18.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 18; number of repdigits = #{99,666,333333,222222222,1^18} = A242627(18) = 5. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235228 n = a235228_list !! (n-1)
a235228_list = filter ((== 18) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 18];

Select[Range[1000], Total[IntegerDigits[#]] == 18 &]

a(n) = 9*A279769(n). - M. F. Hasler, Dec 23 2016

A166370 Numbers whose sum of digits is 17.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Oct 13 2009

A007953(a(n)) = 17; number of repdigits = A242627(17) = 1. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a166370 n = a166370_list !! (n-1)
a166370_list = filter ((== 17) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..900] | &+Intseq(n) eq 17]; // Vincenzo Librandi, Mar 07 2013

Select[Range[900], Total[IntegerDigits[#]] == 17&] (* Vincenzo Librandi, Mar 07 2013 *)

A235225 Numbers whose sum of digits is 14.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 14; number of repdigits = #{77,2222222,1^14} = A242627(14) = 3. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235225 n = a235225_list !! (n-1)
a235225_list = filter ((== 14) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 14];

Select[Range[1000], Total[IntegerDigits[#]] == 14 &]

A235229 Numbers whose sum of digits is 20.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 20; number of repdigits = #{5555,44444,2222222222,1^20} = A242627(20) = 4. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235229 n = a235229_list !! (n-1)
a235229_list = filter ((== 20) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..2000] | &+Intseq(n) eq 20];

Select[Range[2000], Total[IntegerDigits[#]]==20&]

A235226 Numbers whose sum of digits is 15.

Original entry on oeis.org

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

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 15; number of repdigits = #{555,33333,1^15} = A242627(15) = 3. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

a235226 n = a235226_list !! (n-1)
a235226_list = filter ((== 15) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 15];

Select[Range[1000], Total[IntegerDigits[#]] == 15 &]

cp's OEIS Frontend

A052220 Numbers whose sum of digits is 6.

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A166459 Numbers whose sum of digits is 19.

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A143164 Numbers with digitsum 13, in increasing order.

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A235151 Numbers whose sum of digits is 12.

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A235227 Numbers whose sum of digits is 16.

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A235228 Numbers whose sum of digits is 18.

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A166370 Numbers whose sum of digits is 17.

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