A014345 Exponential convolution of primes with themselves.

4, 12, 38, 118, 362, 1082, 3166, 8910, 24426, 64226, 165262, 413418, 1021362, 2490686, 6009150, 14401410, 34098042, 80281962, 187356750, 432549154, 992941250, 2256712462, 5088826238, 11408805862, 25425739346, 56383362854, 124565557898, 274390550594

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^2. - Ilya Gutkovskiy, Mar 10 2018

a(n) = Sum_{j=0..n} binomial(n,j)*prime(j+1)*prime(n-j+1). - G. C. Greubel, Jun 07 2019

Maple

a:= proc(n) option remember; (p-> add(
      p(j+1)*p(n-j+1)*binomial(n, j), j=0..n))(ithprime)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 10 2018

Mathematica

a[n_] := Sum[Prime[j + 1] Prime[n - j + 1] Binomial[n, j], {j, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 05 2018, from Maple *)

Prog

(Magma) [&+[NthPrime(k+1)*NthPrime(n-k+1)*Binomial(n, k): k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Jun 07 2019
(PARI) {a(n) = sum(j=0, n, binomial(n, j)*prime(j+1)*prime(n-j+1))}; \\ G. C. Greubel, Jun 07 2019
(Sage) [sum(binomial(n, j)*nth_prime(j+1)*nth_prime(n-j+1) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 07 2019

Crossrefs

Cf. A000040, A014347, A014352.

Sequence in context: A183159 A369682 A289809 * A006192 A354341 A149324

Adjacent sequences: A014342 A014343 A014344 * A014346 A014347 A014348

Keyword

nonn

Author

N. J. A. Sloane

Status

approved