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

1,3

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

Example

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").

Prog

(PARI) See Links section.

Crossrefs

Cf. A165418, A175466.

Sequence in context: A117649 A028291 A067997 * A034379 A007000 A073472

Adjacent sequences: A175488 A175489 A175490 * A175492 A175493 A175494

Keyword

base,nonn

Author

Leroy Quet, May 28 2010

Extensions

More terms from Lars Blomberg, Feb 25 2016

Status

approved