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%I #13 Jun 17 2018 03:42:07
%S 7,19,23,61,89,149,157,193,239,247,373,377,403,509,523,577,739,767,
%T 769,799,881,1037,1129,1229,1271,1291,1307,1421,1501,1937,1943,1951,
%U 2051,2159,2243,2303,2311,2549,2587,2669,2767,2809,2813,2851,2963,3593,3649
%N Numbers k such that the pair (prime(k) - k)*(prime(k) + k) +- 1 is a twin prime.
%H Harry J. Smith, <a href="/A065749/b065749.txt">Table of n, a(n) for n = 1..1000</a>
%e (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]
%t 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 *)
%o (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
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Nov 21 2001
%E More terms from _Naohiro Nomoto_, Nov 29 2001
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