A064998 a(n) is the smallest prime p such that p*n! +- 1 are twin primes.

2, 2, 3, 2, 17, 7, 7, 3, 61, 29, 167, 401, 167, 19, 311, 461, 97, 919, 47, 71, 1483, 107, 13, 1571, 821, 1361, 769, 239, 163, 4229, 593, 373, 1571, 173, 6229, 3331, 1879, 2837, 2633, 12329, 2311, 269, 4159, 1217, 9719, 509, 3049, 8429, 307, 6121, 7919

Offset

2,1

Links

Harry J. Smith, Table of n, a(n) for n = 2..200

Example

a(6) = 17 because 17*6! = 12240, 12240 + 1 and 12240 - 1 are twin primes, and there is no prime less than 17 for which this pairing will work.

Mathematica

Do[k = 1; While[ !PrimeQ[ Prime[k]*n! - 1] || !PrimeQ[ Prime[k]*n! + 1], k++ ]; Print[ Prime[k]], {n, 2, 75} ]

Prog

(PARI) { allocatemem(932245000); for (n=2, 200, f=n!; p=2; while (!isprime(p*f + 1) || !isprime(p*f - 1), p=nextprime(p + 1)); write("b064998.txt", n, " ", p) ) } \\ Harry J. Smith, Oct 03 2009

Crossrefs

Cf. A051888, A064983.

Sequence in context: A016009 A110088 A322005 * A329352 A300832 A329350

Adjacent sequences: A064995 A064996 A064997 * A064999 A065000 A065001

Keyword

nonn

Author

Robert G. Wilson v, Oct 31 2001

Status

approved