A065749 Numbers k such that the pair (prime(k) - k)*(prime(k) + k) +- 1 is a twin prime.

7, 19, 23, 61, 89, 149, 157, 193, 239, 247, 373, 377, 403, 509, 523, 577, 739, 767, 769, 799, 881, 1037, 1129, 1229, 1271, 1291, 1307, 1421, 1501, 1937, 1943, 1951, 2051, 2159, 2243, 2303, 2311, 2549, 2587, 2669, 2767, 2809, 2813, 2851, 2963, 3593, 3649

Offset

1,1

Links

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

Example

(A000040(23) - 23)*(A000040(23) + 23) +-1 = (83 - 23)*(83 + 23) +- 1 = 6360 +- 1 = (6359, 6361), a twin prime: So a(3) = 23; A065750(3) = 6359. [corrected by Harry J. Smith, Oct 30 2009]

Mathematica

tpQ[n_]:=Module[{np=Prime[n], c}, c=(np-n)(np+n); And@@PrimeQ[{c+1, c-1}]]; Select[Range[4000], tpQ] (* Harvey P. Dale, Sep 05 2012 *)

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("b065749.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 29 2009

Crossrefs

Sequence in context: A141831 A176182 A292349 * A032642 A127633 A055246

Adjacent sequences: A065746 A065747 A065748 * A065750 A065751 A065752

Keyword

nonn

Author

Reinhard Zumkeller, Nov 21 2001

Extensions

More terms from Naohiro Nomoto, Nov 29 2001

Status

approved