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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A279777 Numbers k such that the sum of digits of 9k is 27.

Original entry on oeis.org

111, 211, 221, 222, 311, 321, 322, 331, 332, 333, 411, 421, 422, 431, 432, 433, 441, 442, 443, 444, 511, 521, 522, 531, 532, 533, 541, 542, 543, 544, 551, 552, 553, 554, 555, 611, 621, 622, 631, 632, 633, 641, 642, 643, 644, 651, 652, 653, 654, 655, 661
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

The digital sum of 9k is always a multiple of 9. For most numbers below 100 it is actually equal to 9. Numbers such that the digital sum of 9k is 18 are listed in A279769. Only every third term of the present sequence is divisible by 3.
The sequence of record gaps [and upper end of the gap] is: 100 [a(2) = 211], 101 [a(221) = 1211], 111 [a(4841) = 11211], 111 [a(10121) = 22311], 111 [a(15752) = 33411], ..., 111 [a(45133) = 88911], 111 [a(50413) = 100011], 211 [a(55253) = 111211], 311 [a(110000) = 222311], ..., 911 [a(380557) = 888911], 1011 [a(411049) = 1000011], 1211 [a(436976) = 1111211], 2311 [a(840281) = 2222311], ..., 8911 [a(2451241) = 8888911], ...

Crossrefs

Cf. A008591, A084854, A003991, A004247, A279769 (sumdigits(9n) = 18).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Numbers with given digital sum: 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), A235229 (20).
Cf. A007953 (digital sum), A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Cf. A082259.

Programs

  • Mathematica
    Select[Range@ 661, Total@ IntegerDigits[9 #] == 27 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(9*n)==27

A279768 Numbers n such that the sum of digits of 8n equals 16.

Original entry on oeis.org

11, 47, 56, 74, 83, 92, 101, 110, 119, 137, 146, 173, 182, 191, 209, 218, 227, 245, 272, 281, 299, 308, 317, 326, 335, 344, 353, 398, 407, 416, 434, 443, 452, 470, 479, 488, 506, 524, 533, 542, 551, 560, 569, 578, 605, 614, 632, 641, 659, 668, 677, 695
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088410 = A069543/8 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 700, Total@ IntegerDigits[8 #] == 16 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(8*n)==16

A279775 Numbers k such that the sum of digits of 5k equals 10.

Original entry on oeis.org

11, 29, 38, 47, 56, 65, 74, 83, 92, 101, 110, 128, 146, 164, 182, 209, 218, 227, 236, 245, 254, 263, 272, 281, 290, 308, 326, 344, 362, 380, 407, 416, 425, 434, 443, 452, 461, 470, 488, 506, 524, 542, 560, 605, 614, 623, 632, 641, 650, 668, 686, 704, 722, 740, 803, 812, 821, 830, 848, 866, 884, 902, 920
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088407 = A069540/5 and A279769 (the analog for 9).

Links

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 920, Total@ IntegerDigits[5 #] == 10 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    select( is(n)=sumdigits(5*n)==10, [0..999])
  • Python
    def ok(n): return sum(map(int, str(5*n))) == 10
print([k for k in range(921) if ok(k)]) # Michael S. Branicky, Nov 29 2021

A279770 Numbers n such that the sum of digits of 7n equals 14.

Original entry on oeis.org

11, 38, 47, 56, 65, 74, 83, 92, 101, 110, 119, 155, 164, 182, 191, 209, 218, 236, 245, 263, 272, 299, 308, 317, 326, 335, 344, 353, 362, 380, 389, 416, 434, 452, 461, 470, 479, 488, 506, 515, 533, 560, 578, 587, 596, 605, 623, 632, 650, 659, 686, 722, 731
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088409 = A063416/7 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 731, Total@ IntegerDigits[7 #] == 14 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(7*n)==14

A279772 Numbers n such that the sum of digits of 2n equals 4.

Original entry on oeis.org

2, 11, 20, 56, 65, 101, 110, 155, 200, 506, 515, 551, 560, 605, 650, 1001, 1010, 1055, 1100, 1505, 1550, 2000, 5006, 5015, 5051, 5060, 5105, 5150, 5501, 5510, 5555, 5600, 6005, 6050, 6500, 10001, 10010, 10055, 10100, 10505, 10550, 11000, 15005, 15050, 15500
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088404 = A069537/2 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A052216 (sumdigits(n) = 2), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 15500, Total@ IntegerDigits[2 #] == 4 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    select( is(n)=sumdigits(2*n)==4, [1..9999])

A279773 Numbers n such that the sum of digits of 3n equals 6.

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 20, 35, 38, 41, 44, 47, 50, 68, 71, 74, 77, 80, 101, 104, 107, 110, 134, 137, 140, 167, 170, 200, 335, 338, 341, 344, 347, 350, 368, 371, 374, 377, 380, 401, 404, 407, 410, 434, 437, 440, 467, 470, 500, 668, 671, 674, 677, 680, 701
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088405 = A052217/3 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 720, Total@ IntegerDigits[3 #] == 6 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    select( is(n)=sumdigits(3*n)==6, [1..999])

A279774 Numbers n such that the sum of digits of 4n equals 8.

Original entry on oeis.org

2, 11, 20, 29, 38, 56, 65, 83, 101, 110, 128, 155, 200, 254, 263, 281, 290, 308, 326, 335, 353, 380, 425, 506, 515, 533, 551, 560, 578, 605, 650, 758, 776, 785, 803, 830, 875, 1001, 1010, 1028, 1055, 1100, 1253, 1280, 1325, 1505, 1550, 1775
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088406 = A063997/4 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 2000, Total@ IntegerDigits[4 #] == 8 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    select( is(n)=sumdigits(4*n)==8, [1..1999])

A279776 Numbers n such that the sum of digits of 6n equals 12.

Original entry on oeis.org

8, 11, 14, 23, 26, 29, 32, 38, 41, 44, 47, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 86, 89, 92, 95, 101, 104, 107, 110, 119, 122, 125, 134, 137, 140, 152, 155, 173, 176, 179, 182, 188, 191, 194, 197, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 236
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088408 = A062768/6 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: 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), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 240, Total@ IntegerDigits[6 #] == 12 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(6*n)==12

A304368 Numbers n with additive persistence = 3.

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, 1297
Offset: 1

Views

Author

Jaroslav Krizek, May 11 2018

Keywords

Comments

First deviation from A166459 is at a(101); a(101) = 1999, A166459(101) = 2089.

Examples

			Repeatedly taking the sum of digits starting with 199 gives 19, 10, and then 1. There are three steps, so the additive persistence is 3, and 199 is a member. - _Michael B. Porter_, May 16 2018

Links

Crossrefs

Cf. A031286.
Cf. Numbers with additive persistence k: A304366 (k=1), A304367 (k=2), A304373 (k=4).

Programs

  • Mathematica
    Select[Range@ 1300, Length@ FixedPointList[Total@ IntegerDigits@ # &, #] == 5 &] (* Michael De Vlieger, May 14 2018 *)
  • PARI
    nb(n) = {my(nba = 0); while (n > 9, n = sumdigits(n); nba++); nba;}
isok(n) = nb(n) == 3; \\ Michel Marcus, May 13 2018

Formula

A031286(a(n)) = 3.

A121669 Numbers with sum of digits = 19, divisible by 19 and containing the string "19".

Original entry on oeis.org

17119, 19171, 19342, 19513, 20197, 21907, 33193, 34219, 41914, 51319, 61921, 101935, 102619, 112195, 119035, 119206, 121942, 125191, 171019, 171190, 190171, 190342, 190513, 191026, 191710, 192052, 192223, 193420, 194104, 195130, 195301, 197011, 201970, 204193
Offset: 1

Views

Author

Hassan Taifour (hytaifour(AT)yahoo.co.uk), Sep 10 2006

Keywords

Comments

Conjecture: There are approximately k(n-1)(n-2)^(n-2) terms of this sequence up to 10^n, where k is about e/(19e-19). - Charles R Greathouse IV, Oct 13 2022

Links

Crossrefs

Intersection of A008601, A166459 and A293879.

Programs

  • Mathematica
    d19Q[n_]:=Module[{idn=IntegerDigits[n]},Total[idn]==19&&MemberQ[ Partition[ idn,2,1],{1,9}]]; Select[19*Range[20000],d19Q] (* Harvey P. Dale, Jun 10 2014 *)
  • Python
    def ok(n): s = str(n); return n%19==0 and '19' in s and sum(map(int, s))==19
print(list(filter(ok, range(205000)))) # Michael S. Branicky, Aug 06 2021

Extensions

More terms from Zak Seidov, Sep 12 2006
Previous Showing 21-30 of 33 results. Next

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