1,1

Comments from Jonathan Vos Post (jvospost3(AT)gmail.com), May 17 2006 (Start): Could be defined as "Numbers n such that k^3+k^2+n is prime for k = 0, 1, 2."

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. (End)

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

{n such that n prime, n+2 prime, n+12 prime} = A001359 INTERSECT A046133. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 17 2006

Cf. A000040, A001359, A046133, A050266.

Sequence in context: A046869 A028388 A067606 this_sequence A162336 A074267 A068072

Adjacent sequences: A046132 A046133 A046134 this_sequence A046136 A046137 A046138

nonn

Eric Weisstein (eric(AT)weisstein.com)

Edited by R. J. Mathar and N. J. A. Sloane (njas(AT)research.att.com), Aug 13 2008