A062688 Smallest triangular number with digit sum n (or 0 if no such number exists).

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

1,3

Comments

From Jon E. Schoenfield, Dec 04 2021: (Start)

a(n) = 0 iff n == (2,4,5,7,8) mod 9.

Nonzero terms are not nondecreasing; e.g., a(9)=36 > a(10)=28.

(End)

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..168

Example

66 is the smallest triangular number with digit sum 12, so a(12)=66.

Mathematica

(With[{tbl={#, Total[IntegerDigits[#]]}&/@Accumulate[Range[9000]]}, Table[SelectFirst[ tbl, #[[2]] ==n&], {n, 60}]]/.Missing["NotFound"]->{0, 0})[[;; , 1]] (* Harvey P. Dale, Aug 21 2024 *)

Prog

(PARI) a(n) = if (vecsearch([2, 4, 5, 7, 8], n % 9), return (0)); my(k=1); while (sumdigits(k*(k+1)/2) != n, k++); k*(k+1)/2; \\ Michel Marcus, Dec 12 2021

Crossrefs

Cf. A000217, A007953, A055264, A068808.

Sequence in context: A194498 A193986 A376203 * A067181 A321429 A145225

Adjacent sequences: A062685 A062686 A062687 * A062689 A062690 A062691

Keyword

base,nonn

Author

Erich Friedman, Jul 04 2001

Status

approved