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

1,1

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 *)

Prog

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

Crossrefs

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

Sequence in context: A043365 A023738 A070799 * A031474 A045203 A313082

Adjacent sequences: A277545 A277546 A277547 * A277549 A277550 A277551

Keyword

nonn,easy

Author

Clark Kimberling, Oct 20 2016

Status

approved