0,5

Binomial transform of sequence (0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0). Note: the binomial transform of the sequence (0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0) is A111926; the binomial transform of the sequence (0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0) is A024495 (disregarding first two terms, which are both zero).

The sequence relates the calculation of the logarithm of the Twin Prime Constants of order 3 to the sequence of prime zeta functions, see definition 7 in arXiv:0903.2514. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 28 2009]

a(n+2) - a(n+1) + a(n) = A000225(n);

seq(sum(binomial(n, k*3), k=1..n), n=0..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com)), Oct 23 2007

Cf. A000295, A111926, A024495.

Sequence in context: A132925 A166553 A053643 this_sequence A109885 A054211 A112770

Adjacent sequences: A111924 A111925 A111926 this_sequence A111928 A111929 A111930

easy,nonn

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 21 2005