A065750 - OEIS

%I #14 Jun 18 2018 03:26:02

%S 239,4127,6359,76367,204599,715679,819911,1333991,2189879,2394479,

%T 6358271,6571151,7493879,12968687,13871591,17450159,31072007,33552359,

%U 33642839,36950759,46023119,67300991,81589967,97950287,105652007

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

%H Harry J. Smith, <a href="/A065750/b065750.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (A000040(A065749(n)) - A065749(n))*(A000040(A065749(n)) + A065749(n)) - 1. [corrected by _Harry J. Smith_, Oct 30 2009]

%e 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]

%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("b065750.txt", n++, " ", b - 1); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 30 2009

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 21 2001

%E More terms from _Naohiro Nomoto_, Nov 29 2001

%E Offset changed from 0 to 1 by _Harry J. Smith_, Oct 30 2009