A096280 - OEIS

%I #37 Nov 07 2023 05:02:07

%S 2,5,13,83,2707,71475193,674721797,6245693407,118543624847,

%T 82736199371081,72298621492552303967009812018997,

%U 2454725173623452943975951834280921,59966692897276736774965300014477948187539553

%N Primes in A007443 (= binomial transform of primes).

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

%C 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

%H Paolo Xausa, <a href="/A096280/b096280.txt">Table of n, a(n) for n = 1..20</a> (terms 1..17 from M. F. Hasler)

%F a(n) = A007443(A287915(n)). - _M. F. Hasler_, Jun 02 2017

%t A007443[n_]:=Sum[Binomial[n-1,k-1]Prime[k],{k,n}];

%t With[{upto=500},Select[Array[A007443,upto],PrimeQ]] (* or *)

%t 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 *)

%o (PARI) \\ n = terms to add, m = order.

%o 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); }

%o (PARI) for(n=1,999, ispseudoprime(A007443(n))&&print1(A007443(n)",")) \\ _M. F. Hasler_, Jun 02 2017

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

%Y See A287915 for the corresponding indices of A007443.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 23 2004

%E Definition corrected, initial term 2 added, and edited by _M. F. Hasler_, Jun 02 2017

%E Name simplified by _Paolo Xausa_, Nov 05 2023