A023538 Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.

1, 4, 10, 21, 39, 68, 110, 169, 247, 348, 478, 639, 837, 1076, 1358, 1687, 2069, 2510, 3012, 3581, 4221, 4934, 5726, 6601, 7565, 8626, 9788, 11053, 12425, 13906, 15500, 17221, 19073, 21062, 23190, 25467, 27895, 30480, 33228, 36143, 39231, 42498, 45946, 49585

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• F. Javier de Vega, An extension of Furstenberg's theorem of the infinitude of primes, arXiv:2003.13378 [math.NT], 2020.

Crossrefs

Cf. A007504, A014148, A014150, A014284, A023538, A178138.

Programs

Mathematica

Nest[Accumulate,Join[{1},Select[Range@200,PrimeQ]],2] (* Vladimir Joseph Stephan Orlovsky, Jan 25 2012 *)

Formula

a(n) = Sum_{k<=n} [(A158611(k+1)) * (A000027(n-k+1))] = Sum_{k<=n} [(A008578(k)) * (A000027(n-k+1))]. [Jaroslav Krizek, Aug 05 2009; Correction for change of offset in A158611 and A008578 in Aug 2009 Jaroslav Krizek, Jan 27 2010]