%I #33 Feb 09 2021 01:54:39

%S 4,9,14,19,20,24,29,34,39,44,45,49,54,59,64,69,70,74,79,84,89,94,95,

%T 99,100,104,109,114,119,120,124,129,134,139,144,145,149,154,159,164,

%U 169,170,174,179,184,189,194,195,199,204,209,214,219,220,224,225,229

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

%C Positions of 4 in A277543. Numbers that have 4 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. All these sequences have the same density of 1/4.

%C 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

%H Clark Kimberling, <a href="/A277548/b277548.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: a(n) = 4*n if and only if n is in A033042. - _David A. Corneth_, Oct 23 2016

%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 == 4; \\ _Michel Marcus_, Oct 21 2016

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

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Oct 20 2016