A173757 Numbers k such that exactly one of k^2 + k + 1 and k^2 + k + 11 is prime.

0, 4, 7, 9, 13, 14, 16, 18, 21, 23, 24, 25, 27, 28, 29, 30, 33, 34, 39, 45, 47, 50, 51, 52, 54, 56, 57, 58, 59, 60, 61, 66, 67, 68, 69, 71, 73, 77, 81, 83, 84, 85, 89, 90, 93, 94, 96, 99, 100, 103, 105, 106, 108, 110, 111, 113, 114, 117, 119, 122, 123, 124, 125, 127, 130

Offset

1,2

Comments

Numbers k such that either k^2+k+1 or k^2+k+11 is prime, but not both. - R. J. Mathar, Mar 01 2010

Links

Table of n, a(n) for n=1..65.

Example

0 is in the sequence because 0^2+0+1 = 1 is nonprime and 0^2+0+11 = 11 is prime; 1 is not in the sequence because 1^2+1+1 = 3 is prime and 1^2+1+11 = 13 is also prime, 10 is not in the sequence because 10^2+10+1 = 111 is nonprime and 10^2+10+11 = 121 is also nonprime; 14 is in the sequence because 14^2+14+1 = 211 is prime and 14^2+14+11 = 221 is nonprime.

Prog

(Magma) [ n: n in [0..130] | IsPrime(k+1) ne IsPrime(k+11) where k is n^2+n ]; // Klaus Brockhaus, Feb 26 2010

Crossrefs

Cf. A048058.

Sequence in context: A257803 A310956 A310957 * A307175 A310958 A310959

Adjacent sequences: A173754 A173755 A173756 * A173758 A173759 A173760

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 23 2010

Extensions

Edited and extended by Klaus Brockhaus, Feb 26 2010

More terms from R. J. Mathar, Mar 01 2010

Status

approved