A037310 Numbers whose base-3 and base-5 expansions have the same digit sum.

1, 2, 6, 7, 8, 10, 11, 15, 16, 17, 20, 30, 31, 32, 40, 41, 55, 56, 60, 61, 62, 65, 70, 71, 78, 79, 100, 101, 105, 106, 107, 129, 135, 136, 137, 141, 142, 143, 145, 146, 153, 154, 159, 170, 177, 178, 179, 180, 181, 182, 186, 187, 188

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Also, numbers n such that the exponent of the largest power of 3 dividing n! is exactly twice the exponent of the largest power of 5 dividing n!. - Ivan Neretin, May 21 2015

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037301 (similar, based upon 2 and 3).

Cf. A053735, A053824.

Programs

Maple

select(t -> convert(convert(t,base,3),`+`)=convert(convert(t,base,5),`+`), [$1..1000]); # Robert Israel, May 21 2015

Mathematica

Select[Range[200],Total[IntegerDigits[#,3]]==Total[IntegerDigits[#,5]]&] (* Harvey P. Dale, Jun 06 2016 *)

PARI

is(n)=sumdigits(n,3)==sumdigits(n,5) \\ Charles R Greathouse IV, May 21 2015

Formula

A053735(a(n)) = A053824(a(n)). - Robert Israel, May 21 2015