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

Offset: 1

Author

Clark Kimberling, Oct 20 2016

Keywords

• nonn
• easy

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

Crossrefs

Cf. A033042, A277543, A277550, A277551, A277555.

Programs

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 *)

PARI

isok(n) = n/5^valuation(n, 5) % 5 == 4; \\ Michel Marcus, Oct 21 2016

Formula

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