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A062688
Smallest triangular number with digit sum n (or 0 if no such number exists).
5
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
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
KEYWORD
base,nonn
AUTHOR
Erich Friedman, Jul 04 2001
STATUS
approved