A385353 Numbers k such that i^(k-i) has digit sum k for at least one i, 1 <= i <= k.

1, 4, 7, 8, 9, 10, 16, 17, 18, 19, 45, 54, 71, 72, 81, 89, 90, 99, 107, 125, 126, 136, 143, 144, 152, 171, 172, 180, 197, 199, 202, 216, 225, 234, 235, 238, 253, 261, 262, 280, 296, 306, 341, 351, 352, 359, 361, 376, 379, 386, 397, 409, 413, 422, 423, 430, 432, 440, 445, 451, 467, 475, 484, 486

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..232

Example

a(6) = 10 is a term because 7^3 = 343 and 8^2 = 64 have digit sum 10.

Maple

filter:= proc(s)
   select(t -> convert(convert(t^(s-t), base, 10), `+`) = s, [$1..s]) <> []
end proc:
select(filter, [$1..1000]);

Mathematica

A385353Q[k_] := AnyTrue[Range[k], Total[IntegerDigits[#^(k - #)]] == k &];
Select[Range[500], A385353Q] (* Paolo Xausa, Jun 30 2025 *)

Prog

(PARI) isok(k) = for (i=1, k, if(sumdigits(i^(k-i)) == k, return(1))); \\ Michel Marcus, Jun 29 2025

Crossrefs

Cf. A007953.

Sequence in context: A180692 A004710 A060257 * A262874 A309264 A161986

Adjacent sequences: A385350 A385351 A385352 * A385354 A385355 A385356

Keyword

nonn,base

Author

Robert Israel, Jun 26 2025

Status

approved