cp's OEIS Frontend

A175491 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.

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