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%I #14 Feb 05 2020 14:26:25
%S 1,1,2,4,7,11,17,25,35,49,64,89,122,174,235,286,334,407,473,581,690,
%T 824,976,1206,1449,1811,2183,2718,3306,4173,5070,5659,6071,6769,7279,
%U 8137,8716,9765,10587,11907,12940,14631,15649,17600,19231,21729,24004,27228
%N a(1)=1. a(n+1) = Sum_{k=1..n} a(b(k,n)), where b(k,n) is the largest positive integer that, when written in binary, occurs as a substring in both binary k and binary n.
%H Rémy Sigrist, <a href="/A175491/b175491.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A175491/a175491.png">Logarithmic scatterplot of the first differences of the first 10000 terms</a>
%H Rémy Sigrist, <a href="/A175491/a175491.gp.txt">PARI program for A175491</a>
%e a(6)=11 because 5=(101)2 and
%e for k=1=(1)2 CS (1)2 and a(1)=1
%e for k=2=(10)2 CS (10)2=2 and a(2)=1
%e for k=3=(11)2 CS (1)2 and a(1)=1
%e for k=4=(100)2 CS (10)2=2 and a(2)=1
%e for k=5=(101)2 CS (101)2=5 and a(5)=7
%e and the sum of these 5 terms is 11.
%e (CS stands for "largest common substring is").
%o (PARI) See Links section.
%Y Cf. A165418, A175466.
%K base,nonn
%O 1,3
%A _Leroy Quet_, May 28 2010
%E More terms from _Lars Blomberg_, Feb 25 2016
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