A065750 Smaller term of a pair of twin primes of form (prime(i) - i)*(prime(i) + i) +- 1; the i is from A065749.

239, 4127, 6359, 76367, 204599, 715679, 819911, 1333991, 2189879, 2394479, 6358271, 6571151, 7493879, 12968687, 13871591, 17450159, 31072007, 33552359, 33642839, 36950759, 46023119, 67300991, 81589967, 97950287, 105652007

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n) = (A000040(A065749(n)) - A065749(n))*(A000040(A065749(n)) + A065749(n)) - 1. [corrected by Harry J. Smith, Oct 30 2009]

Example

6359 = a(3) and 6361 is a twin prime: a(3) = (A000040(A065749(3)) - A065749(3))*(A000040(A065749(3)) + A065749(3)) - 1 = (A000040(23) - 23)*(A000040(23) -23) - 1 = (83 - 23)*(83 + 23) - 1 = 106*60 - 1 = 6360 - 1 = 6359. [corrected by Harry J. Smith, Oct 30 2009]

Prog

(PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, b=(prime(m) - m) * (prime(m) + m); if (isprime(b - 1) && isprime(b + 1), write("b065750.txt", n++, " ", b - 1); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 30 2009

Crossrefs

Sequence in context: A256378 A256377 A201194 * A201045 A056095 A224261

Adjacent sequences: A065747 A065748 A065749 * A065751 A065752 A065753

Keyword

nonn

Author

Reinhard Zumkeller, Nov 21 2001

Extensions

More terms from Naohiro Nomoto, Nov 29 2001

Offset changed from 0 to 1 by Harry J. Smith, Oct 30 2009

Status

approved