A237514 - OEIS

%I #25 Feb 24 2014 16:24:05

%S 1,4,7,12,15,20,23,26,31,34,39,42,45,50,53,58,61,64,69,72,77,80,85,88,

%T 91,96,99,104,107,110,115,118,123,126,129,134,137,142,145,148,153,156,

%U 161,164,169,172,175,180,183,188,191,194,199,202,207,210,213,218,221,226,229,232,237,240

%N Numbers k such that 2^(k-1) < 3^(m-1) < 2^k < 3^m < 2^(k+1), for some m > 2, a(1) = 1.

%C Exponents of A006899(n) such that A006899(n-1) and A006899(n+1) are both odd.

%C Probably finite? The last term?

%C Subsequence of primes starts 7, 23, 31, 53, 61, 107, 137, 191, 199, 229,...

%C Prime indices of A006899(n) such that A006899(n-1) and A006899(n+1) are both odd: 2, 7, 43, 113, 131, 139, 149, 157, 193, 211, 263, 281, 307, 317, 379,...

%C Let f(n) := floor( n * log(2) / log(3)), then k is in the sequence if and only if k = 1 or f(k - 1) = f(k) - 1 and f(k + 1) = f(k) + 1. - _Michael Somos_, Feb 24 2014

%e a(2) = 4 because k = 4 and 2^(4-1) < 3^(3-1) < 2^4 < 3^3 < 2^(4+1) for m = 3;

%e a(3) = 7 because k = 7 and 2^(7-1) < 3^(4-1) < 2^7 < 3^4 < 2^(7+1) for m = 4;

%e a(4) = 12 because k = 12 and 2^(12-1) < 3^(8-1) < 2^12 < 3^8 < 2^(12+1) for m = 8.

%Y Cf. A006899 (numbers of the form 2^i or 3^j).

%K nonn

%O 1,2

%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Feb 08 2014