1,1

The following subset is also prime for k = 3: 5, 11, 17, 71, 101, 137, 227, 281, 347, 431, 641, 827, 1151, 1277, 1487. The following subset of those is also prime for k = 4: 17, 71, 101, 227, 827, 1151, 1487. The following subset of those is also prime for k = 5: 827, 1151, 1487. The "17" in A050266's n^3+n^2+17 is because k^3+k^2+17 is prime for k = 1,2,3,4,5,6,7,8,9,10. Between 10000 and 20000 there are 30 members of the k=0,1,2 sequence, of which these 10 are also prime for k = 3: 10301, 10937, 11057, 11777, 12107, 13997, 15137, 15737, 16061, 19541. The following subset of those is also prime for k = 5: 15137, 15737, 16061. Somewhere in these sequences is a value that breaks the 11-term record of A050266, and indeed any known Prime-Generating Polynomial record. See also: A001359 Lesser of twin primes. See also: A046133 p and p+12 are both prime. See also: A050266 Primes of the form n^3+n^2+17.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

{n such that n prime, n+2 prime, n+12 prime} = A001359 INTERSECT A046133.

Cf. A000040, A001359, A046133, A050266.

Sequence in context: A046869 A028388 A067606 this_sequence A046135 A074267 A068072

Adjacent sequences: A118622 A118623 A118624 this_sequence A118626 A118627 A118628

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), May 17 2006