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.

1, 1, 2, 4, 7, 11, 17, 25, 35, 49, 64, 89, 122, 174, 235, 286, 334, 407, 473, 581, 690, 824, 976, 1206, 1449, 1811, 2183, 2718, 3306, 4173, 5070, 5659, 6071, 6769, 7279, 8137, 8716, 9765, 10587, 11907, 12940, 14631, 15649, 17600, 19231, 21729, 24004, 27228

Offset: 1

Author

Leroy Quet, May 28 2010

Keywords

• base
• nonn

Examples

			a(6)=11 because 5=(101)2 and
for k=1=(1)2 CS (1)2 and a(1)=1
for k=2=(10)2 CS (10)2=2 and a(2)=1
for k=3=(11)2 CS (1)2 and a(1)=1
for k=4=(100)2 CS (10)2=2 and a(2)=1
for k=5=(101)2 CS (101)2=5 and a(5)=7
and the sum of these 5 terms is 11.
(CS stands for "largest common substring is").
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of the first differences of the first 10000 terms
• Rémy Sigrist, PARI program for A175491

Crossrefs

Cf. A165418, A175466.

Programs

PARI

See Links section.

Extensions

More terms from Lars Blomberg, Feb 25 2016