A123341 a(1) = 1, a(n) = Sum_{k=1}^{Pi(n)} a(n-k) for n > 1, where Pi(n) is the number of primes less than or equal to n.

1, 1, 2, 3, 6, 11, 22, 42, 81, 156, 312, 613, 1226, 2430, 4818, 9555, 19110, 38064, 76128, 151944, 303275, 605324, 1210648, 2418866, 4832914, 9656273, 19293436, 38548808, 77097616, 154119104, 308238208, 616324472, 1232345669, 2464086014

Offset

1,3

Comments

Conjecture: lim_{n->infinity} a(n)/2^n > 0; appears to be about 0.1432645404.

Links

Table of n, a(n) for n=1..34.

Formula

a(1) = a(2) = 1, for p an odd prime, a(p) = 2a(p-1), otherwise a(n) = 2a(n-1) - a(n - pi(n) - 1).

Crossrefs

Cf: A000720, A000045, A001590.

Sequence in context: A018613 A036589 A251656 * A238351 A043328 A141072

Adjacent sequences: A123338 A123339 A123340 * A123342 A123343 A123344

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 11 2006

Status

approved