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

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

Offset: 1

Author

Cino Hilliard, Jun 23 2004

Keywords

• nonn

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)

Crossrefs

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

See A287915 for the corresponding indices of A007443.

Programs

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 *)

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

Formula

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

Extensions

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

Name simplified by Paolo Xausa, Nov 05 2023