cp's OEIS Frontend

A144908 Composite numbers n such that sqrt(n) > A144907(n) and absolute normalized digital mean |dm(b, n) * 2 / (b - 1)| decreases for b in [2, k] for some k > 2.

%I A144908 #2 Mar 31 2012 10:28:53
%S A144908 32,64,125,128,192,250,256,288,343,375,384,500,512,576,640,648,768,
%T A144908 800,896,1024,1029,1125,1152,1280,1296,1536,1568,1600,1715,1792,1875,
%U A144908 2025,2048,2058,2304,2401,2500,2560,2592,2816,3072,3136,3200,3328,3375,3456
%N A144908 Composite numbers n such that sqrt(n) > A144907(n) and absolute normalized digital mean |dm(b, n) * 2 / (b - 1)| decreases for b in [2, k] for some k > 2.
%C A144908 Subset of A144100.
%C A144908 Believed to have particular importance for linear congruential pseudorandom number generators.
%e A144908 125 is a member: A144907(125) is 5, which is less than 11.18, the square root of 125;
%e A144908 125 in base 2 is 1111101; dm(2, 125) = (6 * 1 - 1) / 14 = 5/14 ~ 0.357;
%e A144908 125 in base 3 is 11122; dm(3, 125) = (3 * 0 + 2 * 2) / 10 = 2/5 = 0.4;
%e A144908 125 in base 4 is 1331; dm(4, 125) = (2 * -1 + 2 * 3) / 8 = 1/2 = 0.5;
%e A144908 5/14 * 2 / 1 = 5/7 ~ 0.714;
%e A144908 2/5 * 2 / 2 = 2/5 = 0.4;
%e A144908 1/2 * 2 / 3 = 1/3 ~ 0.333;
%e A144908 For b in [2, 4], |dm(b, 125) * 2 / (b - 1)| is decreasing.
%Y A144908 Cf. A144100, A144907, A144777
%K A144908 base,easy,nonn
%O A144908 1,1
%A A144908 _Reikku Kulon_, Sep 24 2008