A096280 Primes in A007443 (= binomial transform of primes).

2, 5, 13, 83, 2707, 71475193, 674721797, 6245693407, 118543624847, 82736199371081, 72298621492552303967009812018997, 2454725173623452943975951834280921, 59966692897276736774965300014477948187539553

Offset

1,1

Comments

Sum of reciprocals = 0.2893406979695919267175673140... Are these primes infinite?

The next term is too large to be displayed here. See A287915 for the indices k which yield these primes A007443(k). - M. F. Hasler, Jun 02 2017

Links

Paolo Xausa, Table of n, a(n) for n = 1..20 (terms 1..17 from M. F. Hasler)

Formula

a(n) = A007443(A287915(n)). - M. F. Hasler, Jun 02 2017

Mathematica

A007443[n_]:=Sum[Binomial[n-1, k-1]Prime[k], {k, n}];
With[{upto=500}, Select[Array[A007443, upto], PrimeQ]] (* or *)
Module[{upto=500, b}, b=Prime[Range[upto]]; Join[{2}, Select[Table[First[b=ListConvolve[{1, 1}, b]], upto-1], PrimeQ]]] (* Paolo Xausa, Oct 31 2023 *)

Prog

(PARI) \\ n = terms to add, m = order.
sucsumspr(n, m) = { local(a, b, i, j, k, sr); sr=0; a = primes(1001); b = vector(1001); for(i=1, m, for(j=1, n+n, b[j] = a[j]+ a[j+1]; ); a=b; if(isprime(a[1]), print1(a[1]", "); sr+=1.0/a[1]); ); print(); print(sr); }
(PARI) for(n=1, 999, ispseudoprime(A007443(n))&&print1(A007443(n)", ")) \\ M. F. Hasler, Jun 02 2017

Crossrefs

Cf. A007443, A287915, A001043, A096277, A096278, A096279.

See A287915 for the corresponding indices of A007443.

Sequence in context: A081650 A092262 A365326 * A236395 A032015 A325626

Adjacent sequences: A096277 A096278 A096279 * A096281 A096282 A096283

Keyword

nonn

Author

Cino Hilliard, Jun 23 2004

Extensions

Definition corrected, initial term 2 added, and edited by M. F. Hasler, Jun 02 2017

Name simplified by Paolo Xausa, Nov 05 2023

Status

approved