A065564 - OEIS

A065564

Numbers k such that floor((4/3)^(k+1))/floor((4/3)^k) = 4/3.

4, 13, 18, 20, 21, 23, 24, 34, 44, 45, 49, 56, 60, 63, 65, 66, 67, 79, 81, 83, 85, 88, 94, 102, 107, 109, 119, 125, 126, 129, 131, 132, 133, 135, 138, 139, 144, 161, 162, 164, 172, 174, 175, 190, 194, 199, 204, 217, 218, 233, 234, 240, 249, 250, 253, 255, 258

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith).

FORMULA

Lim_{n->infinity} a(n)/n = 4?

MATHEMATICA

A065564Q[k_] := 3*Floor[#*4/3] == 4*Floor[#] & [(4/3)^k];

Select[Range[300], A065564Q] (* Paolo Xausa, Nov 11 2025 *)

PROG

(PARI) isok(k) = { my(f=4/3); floor(f^(k + 1))/floor(f^k) == f } \\ Harry J. Smith, Oct 22 2009