login
Numbers k such that k/5^m == 3 (mod 5), where 5^m is the greatest power of 5 that divides k.
5

%I #25 Feb 09 2021 01:54:47

%S 3,8,13,15,18,23,28,33,38,40,43,48,53,58,63,65,68,73,75,78,83,88,90,

%T 93,98,103,108,113,115,118,123,128,133,138,140,143,148,153,158,163,

%U 165,168,173,178,183,188,190,193,198,200,203,208,213,215,218,223,228

%N Numbers k such that k/5^m == 3 (mod 5), where 5^m is the greatest power of 5 that divides k.

%C Positions of 3 in A277543. Numbers that have 3 as their rightmost nonzero digit when written in base 5.

%C This is one sequence in a 4-way splitting of the positive integers; the other three are indicated in the Mathematica program.

%H Clark Kimberling, <a href="/A277555/b277555.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t p[5, 1] (* A277550 *)

%t p[5, 2] (* A277551 *)

%t p[5, 3] (* A277555 *)

%t p[5, 4] (* A277548 *)

%o (PARI) isok(n) = n/5^valuation(n, 5) % 5 == 3; \\ _Michel Marcus_, Oct 20 2016

%Y Cf. A132739, A277543, A277550, A277551, A277548.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Oct 20 2016