cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A204399 Numbers k such that floor(2^k / 3^n) = 1.

This page as a plain text file.
%I A204399 #24 Dec 09 2022 19:36:06
%S A204399 0,2,4,5,7,8,10,12,13,15,16,18,20,21,23,24,26,27,29,31,32,34,35,37,39,
%T A204399 40,42,43,45,46,48,50,51,53,54,56,58,59,61,62,64,65,67,69,70,72,73,75,
%U A204399 77,78,80,81,83,85,86,88,89,91,92,94,96,97,99,100,102,104
%N A204399 Numbers k such that floor(2^k / 3^n) = 1.
%C A204399 Presumably a(n) ~ 3*n - floor(n*sqrt(2)) = A195176(n). In the first hundred, a(n) = A195176(n) except for n = 41, 70, 82, 94 where a(n) = A195176(n) - 1.
%C A204399 The conjecture is false; A195176(n) - a(n) increases without bound (though not monotonically) since log_2(3) < 3 - sqrt(2). - _Charles R Greathouse IV_, Jan 15 2012
%C A204399 Basically a duplicate of A020914. - _R. J. Mathar_, Jan 16 2012
%F A204399 a(n) = ceiling( n * log_2(3) ). - _Charles R Greathouse IV_, Jan 15 2012
%p A204399 for n from 0 to 120 do : for k from 0 to 100 do: x:=floor(2^k /3^n):if x=1 then printf(`%d, `,k):else fi:od:od:
%o A204399 (PARI) a(n)=ceil(n*log(3)/log(2)) \\ _Charles R Greathouse IV_, Jan 15 2012
%Y A204399 Cf. A020914, A056576.
%K A204399 nonn
%O A204399 0,2
%A A204399 _Michel Lagneau_, Jan 15 2012