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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, 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
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
Sequence in context: A117649 A028291 A067997 * A034379 A007000 A073472
KEYWORD
base,nonn
AUTHOR
Leroy Quet, May 28 2010
EXTENSIONS
More terms from Lars Blomberg, Feb 25 2016
STATUS
approved