A277567 Numbers k such that k/6^m == 1 (mod 6), where 6^m is the greatest power of 6 that divides k.

1, 6, 7, 13, 19, 25, 31, 36, 37, 42, 43, 49, 55, 61, 67, 73, 78, 79, 85, 91, 97, 103, 109, 114, 115, 121, 127, 133, 139, 145, 150, 151, 157, 163, 169, 175, 181, 186, 187, 193, 199, 205, 211, 216, 217, 222, 223, 229, 235, 241, 247, 252, 253, 258, 259, 265

Offset: 1

Author

Clark Kimberling, Nov 01 2016

Keywords

• nonn
• easy

Comments

Positions of 1 in A277544. Numbers having 1 as rightmost nonzero digit in base 6. This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program.

Links

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

Crossrefs

Cf. A277544, A277568, A277569.

Programs

Mathematica

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* A277569 *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)
Select[Range[300],Mod[#/6^IntegerExponent[#,6],6]==1&] (* Harvey P. Dale, Sep 27 2023 *)

PARI

is(n)=(n/6^valuation(n,6))%6==1 \\ Charles R Greathouse IV, Nov 03 2016

Formula

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016