A062688 -id:A062688 - cp's OEIS frontend

A067181 Duplicate of A062688.

0, 1, 0, 3, 0, 0, 6, 0, 0, 36, 28, 0, 66, 0, 0, 78, 0, 0, 378, 496, 0, 1596, 0, 0, 8385, 0, 0, 5778, 5995, 0, 8778, 0, 0, 47895, 0, 0, 67896, 58996, 0, 196878, 0, 0, 468996, 0, 0, 887778, 1788886, 0, 4896885, 0, 0, 5897895, 0, 0, 13999986, 15997996, 0, 38997696

Offset: 0

Amarnath Murthy, Jan 09 2002

dead

Cf. A055264.

a(n) = A062688(n), n > 0. - R. J. Mathar, Sep 30 2008

More terms from Sascha Kurz, Mar 23 2002

A004157 Sum of digits of n-th triangular number.

Original entry on oeis.org

0, 1, 3, 6, 1, 6, 3, 10, 9, 9, 10, 12, 15, 10, 6, 3, 10, 9, 9, 10, 3, 6, 10, 15, 3, 10, 9, 18, 10, 12, 15, 19, 15, 12, 19, 9, 18, 10, 12, 15, 10, 15, 12, 19, 18, 9, 10, 12, 15, 10, 15, 12, 19, 9, 18, 10, 21, 15, 10, 15, 12, 19, 18, 9, 10, 12, 6, 19, 15, 12, 19, 18, 18, 10, 21, 15, 19, 6, 12, 10

Offset: 0

N. J. A. Sloane

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A000217, A007953, A062688, A145389.

[&+Intseq(n*(n+1) div 2): n in [0..80] ]; // Vincenzo Librandi, Jun 18 2015

seq(convert(convert(n*(n+1)/2,base,10),`+`), n=0..100); # Robert Israel, Jun 18 2015

Table[Plus@@IntegerDigits@(n (n + 1) / 2), {n, 0, 90}] (* Vincenzo Librandi, Jun 18 2015 *)
Total[IntegerDigits[#]]&/@Accumulate[Range[0,100]] (* Harvey P. Dale, Mar 31 2024 *)

a(n) = sumdigits(n*(n+1)/2); \\ Michel Marcus, Jun 18 2015

a(n) = A007953(A000217(n)). - Robert Israel, Jun 18 2015

A068129 Triangular numbers with sum of digits = 10.

Original entry on oeis.org

28, 55, 91, 136, 190, 253, 325, 406, 703, 820, 1081, 1225, 1540, 1711, 2080, 2701, 3160, 3403, 5050, 7021, 10153, 11026, 12403, 15400, 17020, 20503, 21115, 23005, 24310, 32131, 41041, 51040, 52003, 60031, 72010, 80200, 90100, 106030, 110215

Offset: 1

Amarnath Murthy, Feb 21 2002

1. The sequence is unbounded, as the (2*10^k +2)-th triangular number is a term. 2. The sum of the digits of triangular numbers in most cases is a triangular number. 3. Conjecture: For every triangular number T there exist infinitely many triangular numbers with sum of digits = T.

The second assertion above is wrong. Out of the first 100,000 triangular numbers, only 26,046 have a sum of their digits equal to a triangular number. - Harvey P. Dale, Jun 07 2017

Robert Israel, Table of n, a(n) for n = 1..164

Intersection of A000217 and A052224.

Cf. A062688, A068127, A068128.

for i from 1 to 9 do S[1,i]:= [i] od: S[1,10]:= []:
R:= NULL: count:= 0:
for d from 2 while count < 100 do
  for i from 1 to 10 do
    S[d,i]:= [seq(op(map(t -> 10*t + j, S[d-1,i-j])),j=0..i-1)];
  od:
  V:= select(t -> issqr(8*t+1), S[d,10]);
  if nops(V) > 0 then
    V:= sort(V);
    R:= R,op(V); count:= count+nops(V);
  fi
od:
R; # Robert Israel, May 15 2025

Select[Accumulate[Range[1000]],Total[IntegerDigits[#]]==10&] (* Harvey P. Dale, Jun 07 2017 *)

More terms from Sascha Kurz, Mar 06 2002

Offset changed by Andrew Howroyd, Sep 17 2024

A068808 Triangular numbers with strictly increasing sum of digits.

Original entry on oeis.org

1, 3, 6, 28, 66, 78, 378, 496, 1596, 5778, 5995, 8778, 47895, 58996, 196878, 468996, 887778, 1788886, 4896885, 5897895, 13999986, 15997996, 38997696, 88877778, 179977878, 189978778, 398988876, 686999778, 1699998895, 5779898886, 9876799878, 38689969878, 39689699896, 67898888778, 89996788896, 299789989975

Offset: 1

Amarnath Murthy, Mar 06 2002

			a(4) = 28 = 7 * (7 + 1) / 2, which is 7th triangular number with sum of digits = 2 + 8 = 10.  a(5) = 66 = 11 * (11 + 1) / 2, which is 11th triangular number with sum of digits = 6 + 6 = 12. Since  12 > 10, 28 and 66 are in list. - _K. D. Bajpai_, Sep 04 2014

K. D. Bajpai, Table of n, a(n) for n = 1..55

Cf. A000217, A062688.

dig := X->convert((convert(X,base,10)),`+`); T := k->k*(k+1)/2; S := k->seq(dig(T(i)),i=1..k-1); seq(`if`(n>1 and dig(T(n))>max(S(n)), T(n),printf("")),n=1..2000);

t = {}; s = 0; Do[If[(x = Total[IntegerDigits[y = n*(n + 1)/2]]) > s, AppendTo[t, y]; s = x], {n, 120000}]; t (* Jayanta Basu, Aug 06 2013 *)

tri(n)=n*(n+1)/2;
A068808=List; listput(A068808,1,1);
y=2;for(k=1,100000,if(sumdigits(Vec(A068808)[y-1])A068808,tri(k),y);y++)); A068808 \\ Edward Jiang, Sep 04 2014

More terms from Francois Jooste (phukraut(AT)hotmail.com), Mar 10 2002
More terms from Sascha Kurz, Mar 27 2002
a(31) to a(33) from K. D. Bajpai, Sep 04 2014
a(34) to a(36) from Robert Israel, Sep 04 2014

A359003 a(n) is the smallest n-gonal number whose sum of digits is n.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 370, 506, 156, 238, 671, 726, 88, 836, 585, 775, 7337, 5268, 8149, 8555, 8961, 9367, 9773, 15786, 9856, 91964, 65757, 89428, 179960, 47796, 108979, 197945, 86976, 467974, 998516, 259896, 598792, 1737788, 869649, 969991, 1985984, 998676, 3798496, 7979546, 5877696

Offset: 3

Ilya Gutkovskiy, Dec 10 2022

			370 is the smallest 10-gonal number with digit sum 10, so a(10) = 370.

Eric Weisstein's World of Mathematics, Polygonal Number

Cf. A007953, A051885, A062685, A062688, A358930.

p[n_, k_] := (n - 2)*k*(k - 1)/2 + k; a[n_] := Module[{k = 1, pk}, While[Plus @@ IntegerDigits[pk = p[n, k]] != n, k++]; pk]; Array[a, 45, 3] (* Amiram Eldar, Dec 10 2022 *)

cp's OEIS Frontend

A067181 Duplicate of A062688.

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A004157 Sum of digits of n-th triangular number.

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A068129 Triangular numbers with sum of digits = 10.

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A068808 Triangular numbers with strictly increasing sum of digits.

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Maple

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A359003 a(n) is the smallest n-gonal number whose sum of digits is n.

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Mathematica