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%I #15 Jul 05 2024 08:13:12
%S 13,163,2803,3565153,210344143,86915972211813115391953,
%T 4419764102942908730796303703,114681479899746991802547357477494803
%N Primes p such that p+2 is a piptorial number. Also numbers such that A080696(n)- 2 is prime.
%C Piptorial numbers are the partial products of prime-indexed primes.
%C Sum of reciprocals = 0.08341509210884323904648676616...
%C a(9) = A080696(1111) - 2 = 1.0954...*10^4885. - _Amiram Eldar_, Jul 05 2024
%e (Product of first four pips) - 2 = 3*5*11*17 - 2 = 2805 - 2 = 2803, which is prime, so 2803 is in the sequence.
%t seq[kmax_] := Module[{r = 1, p = 1, s = {}}, Do[p = NextPrime[p]; r *= Prime[p]; If[PrimeQ[r - 2], AppendTo[s, r - 2]], {k, 1, kmax}]; s]; seq[20] (* _Amiram Eldar_, Jul 05 2024 *)
%o (PARI) piptorial(n) = { s=0; p=1; for(x=1,n, p=p*prime(prime(x)); if(isprime(p-2),print1(p-2","); s+=1.0/(p-2)) ); print(); print(s) }
%Y Cf. A080696, A090886.
%K nonn
%O 1,1
%A _Cino Hilliard_, Oct 21 2003
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