A383356 a(n) = index of the smallest nonagonal number having the same digital sum as the n-th triangular number.

1, 6, 3, 1, 3, 6, 4, 2, 2, 4, 5, 12, 4, 3, 6, 4, 2, 2, 4, 6, 3, 4, 12, 6, 4, 2, 11, 4, 5, 12, 13, 12, 5, 13, 2, 11, 4, 5, 12, 4, 12, 5, 13, 11, 2, 4, 5, 12, 4, 12, 5, 13, 2, 11, 4, 23, 12, 4, 12, 5, 13, 11, 2, 4, 5, 3, 13, 12, 5, 13, 11, 11, 4, 23, 12, 13, 3, 5, 4, 2, 2, 4

Offset

1,2

Comments

From Robert Israel, Apr 24 2025: (Start)

If n == 0 or 8 (mod 9) then a(n) == 0 or 2 (mod 9).

If n == 1, 4 or 7 (mod 9) then a(n) == 1, 4 or 7 (mod 9).

If n == 2 or 6 (mod 9) then a(n) == 5 or 6 (mod 9).

If n == 3 or 5 (mod 9) then a(n) == 3 or 8 (mod 9). (End)

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

For n = 2, the 2nd triangular number is (2^2+2)/2 = 3, its digital sum is 3 and the smallest nonagonal number having 3 as digital sum is (7*6^2 - 5*6)/2 = 111 whose index is 6, so a(2) = 6.
For n = 16, the 16-th triangular number is (16^2 +16)/2 = 136, its digital sum is 10 and the smallest nonagonal number having 10 as digital sum is (7*4^2 -5*4)/2 = 46 whose index is 4, so a(16) = 4.

Maple

ds:= n -> convert(convert(n, base, 10), `+`):
v:= 0: R:= NULL:
for k from 1 to 200 do
   r:= ds(k*(k+1)/2);
   if assigned(W[r]) then R:= R, W[r]
   else do
     v:= v+1;
     s:= ds(v*(7*v-5)/2);
     if not assigned(W[s]) then W[s]:= v fi;
     if s = r then R:= R, v; break fi;
     od fi od:
R; # Robert Israel, Apr 24 2025

Prog

(PARI) a(n) = my(s=sumdigits((n^2+n)/2)); k=1; while(sumdigits((7*k^2-5*k)/2)!=s, k++); k;

Crossrefs

Cf. A000217, A001106, A007953, A004157.

Sequence in context: A238260 A021617 A140321 * A019979 A085580 A092151

Adjacent sequences: A383353 A383354 A383355 * A383357 A383358 A383359

Keyword

nonn,easy,base

Author

Claude H. R. Dequatre, Apr 24 2025

Status

approved