A277548 - OEIS

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A277548

Numbers k such that k/5^m == 4 (mod 5), where 5^m is the greatest power of 5 that divides k.

4, 9, 14, 19, 20, 24, 29, 34, 39, 44, 45, 49, 54, 59, 64, 69, 70, 74, 79, 84, 89, 94, 95, 99, 100, 104, 109, 114, 119, 120, 124, 129, 134, 139, 144, 145, 149, 154, 159, 164, 169, 170, 174, 179, 184, 189, 194, 195, 199, 204, 209, 214, 219, 220, 224, 225, 229

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OFFSET

1,1

COMMENTS

Positions of 4 in A277543. Numbers that have 4 as their rightmost nonzero digit when written in base 5.

This is one sequence in a 4-way splitting of the positive integers; the other three are indicated in the Mathematica program. All these sequences have the same density of 1/4.

Is there some n with a 3 or a 4 in base 5 such that a(n) = 4n + 1? - David A. Corneth, Oct 23 2016

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

Conjecture: a(n) = 4*n if and only if n is in A033042. - David A. Corneth, Oct 23 2016

MATHEMATICA

z = 200; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]

p[b_, d_] := Flatten[Position[a[b], d]]

p[5, 1] (* A277550 *)

p[5, 2] (* A277551 *)

p[5, 3] (* A277555 *)

p[5, 4] (* A277548 *)