A101636 a(n) = least odd prime p such that (p^(P(n))-1)/(p-1) is prime with P(i) = i-th prime, n>1.
3, 7, 3, 5, 3, 11, 11, 113, 151, 19, 61, 53, 89, 5, 307, 19, 19, 491, 3, 11, 271, 41, 251, 271, 359, 3, 19, 79, 233, 5, 7, 13, 11, 5, 29, 71, 139, 127, 139, 2003, 5, 743, 673, 593, 383, 653, 661, 251, 6389, 2833, 223, 163, 37, 709, 131, 41, 2203, 941, 2707, 13, 1283
Offset: 2
Keywords
Examples
(3^3-1)/2=26/2=13 prime so for P(2) a(2)=3.
Programs
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Mathematica
a = {}; Do[ p1 = Prime[n]; k = 2; While[p2 = Prime[k]; ! PrimeQ[(p2^p1 - 1)/(p2 - 1)], k++ ]; AppendTo[a, p2];, {n, 2, 62}]; a (* Ray Chandler, Jan 27 2005 *) f[n_] := Block[{P = Prime[n], k = 2}, While[p = Prime[k]; !PrimeQ[(p^P - 1)/(p - 1)], k++ ]; Prime[ k]]; Table[ f[n], {n, 2, 62}] (* Robert G. Wilson v, Jan 27 2005 *) -
PARI
a(n) = my(p=3, q=prime(n)); while (!ispseudoprime((p^q-1)/(p-1)), p=nextprime(p+1)); p; \\ Michel Marcus, Mar 21 2023
Extensions
Extended by Ray Chandler and Robert G. Wilson v, Jan 27 2005
Comments