cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Vincenzo Librandi, Oct 14 2009

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a166459 n = a166459_list !! (n-1)
a166459_list = filter ((== 19) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1500] | &+Intseq(n) eq 19]; // Vincenzo Librandi, Sep 13 2013
  • Mathematica
    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

Views

Author

Wolfdieter Lang, Sep 15 2008

Keywords

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

Examples

			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

References

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

Links

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.

Programs

  • Haskell
    a143164 n = a143164_list !! (n-1)
a143164_list = filter ((== 13) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • 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 *)
  • 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]Charles R Greathouse IV, May 30 2019

Formula

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

Views

Author

Vincenzo Librandi, Jan 04 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235151 n = a235151_list !! (n-1)
a235151_list = filter ((== 12) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1000] | &+Intseq(n) eq 12];
  • Mathematica
    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

Views

Author

Vincenzo Librandi, Jan 05 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235227 n = a235227_list !! (n-1)
a235227_list = filter ((== 16) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1000] | &+Intseq(n) eq 16];
  • Mathematica
    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

Views

Author

Vincenzo Librandi, Jan 05 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235228 n = a235228_list !! (n-1)
a235228_list = filter ((== 18) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1000] | &+Intseq(n) eq 18];
  • Mathematica
    Select[Range[1000], Total[IntegerDigits[#]] == 18 &]

Formula

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

Views

Author

Vincenzo Librandi, Oct 13 2009

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a166370 n = a166370_list !! (n-1)
a166370_list = filter ((== 17) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..900] | &+Intseq(n) eq 17]; // Vincenzo Librandi, Mar 07 2013
  • Mathematica
    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

Views

Author

Vincenzo Librandi, Jan 05 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235225 n = a235225_list !! (n-1)
a235225_list = filter ((== 14) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1000] | &+Intseq(n) eq 14];
  • Mathematica
    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

Views

Author

Vincenzo Librandi, Jan 05 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235229 n = a235229_list !! (n-1)
a235229_list = filter ((== 20) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..2000] | &+Intseq(n) eq 20];
  • Mathematica
    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

Views

Author

Vincenzo Librandi, Jan 05 2014

Keywords

Comments

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

Links

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.

Programs

  • Haskell
    a235226 n = a235226_list !! (n-1)
a235226_list = filter ((== 15) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
  • Magma
    [n: n in [1..1000] | &+Intseq(n) eq 15];
  • Mathematica
    Select[Range[1000], Total[IntegerDigits[#]] == 15 &]

A242614 Triangle read by rows: row n contains numbers with sum of digits = n, and not greater than the n-th repunit (cf. A007953 and A002275).

Original entry on oeis.org

0, 1, 2, 11, 3, 12, 21, 30, 102, 111, 4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 301, 310, 400, 1003, 1012, 1021, 1030, 1102, 1111, 5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500, 1004, 1013, 1022
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 16 2014

Keywords

Comments

Number of terms in row n = A242622(n);
T(n,1) = A051885(n);
T(n,A242622(n)) = A002275(n);
for n > 0: number of repdigit terms in row n = A242627(n).

Examples

			The triangle begins:
. 0:  0
. 1:  1
. 2:  2,11
. 3:  3,12,21,30,102,111
. 4:  4,13,22,31,40,103,112,121,130,202, . . . ,1021,1030,1102,1111
. 5:  5,14,23,32,41,50,104,113,122,131, . . . ,11021,11030,11102,11111 .

Links

Crossrefs

Cf. A007953 (sum of digits), A002275 (repunits).
Cf. A011557, A052216, A052217, A052218, A052219, A052220, A052221, A052222, A052223, A052224, A166311, A235151, A143164, A235225, A235226, A235227, A166370, A235228, A166459, A235229.

Programs

  • Haskell
    a242614 n k = a242614_row n !! (k-1)
a242614_row n = filter ((== n) . a007953) [n .. a002275 n]
a242614_tabf = map a242614_row [0..]
  • Mathematica
    Join[{0},Flatten[Table[Select[Range[FromDigits[PadRight[{},n,1]]], Total[ IntegerDigits[ #]] == n&],{n,5}]]] (* Harvey P. Dale, Oct 08 2019 *)
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