A051956 a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 and a(1)*a(2)*...*a(n) - 1 are primes.

4, 15, 17, 19, 29, 57, 77, 285, 318, 354, 379, 405, 520, 521, 595, 625, 938, 1706, 1738, 2085, 2345, 2817, 4319, 4529, 7005, 8207, 8232, 9451, 9839, 11044, 11170, 12386, 12421, 12722, 14153, 15220, 15371, 17052, 17965, 18279, 18811, 19890, 21628, 22667, 22746

Offset: 1

Author

Felice Russo, Dec 21 1999

Keywords

• nice
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..184

Crossrefs

Cf. A051935, A051957.

Programs

Mathematica

a[1] = 4; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, p = Times @@ Array[a, n-1]; If[PrimeQ[k*p+1] && PrimeQ[k*p-1], Print[k]; Return[k]]]; Array[a, 45] (* Jean-François Alcover, Oct 23 2016 *)

PARI

lista(nn) = {my (v = vector(nn)); for (n = 1, nn, if (n == 1, p = 1; k = 0; , p = prod(j=1, n-1, v[j]); k = v[n-1]+1); while (! isprime(p*k+1) || ! isprime(p*k-1), k++); v[n] = k; print1(k, ", "););} \\ Michel Marcus, Sep 28 2013

Extensions

More terms from Michel Marcus, Sep 28 2013