1,1

This is the sequence M defined in a comment to A218825.

Zhi-Wei Sun has conjectured (Nov 07 2012) that for any n>0, there is only a finite number of positive odd integers not of the given form. See arXiv:1211.1588.

Table of n, a(n) for n=1..20.

Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arxiv:1211.1588 [math.NT], 2012-2017.

The exceptionally low values a(3), a(4) and a(15) correspond to the sets:

E(3) = {1,3,5,7,31,73} = { 2n-1: for no prime q, both p=2n-1-2q and p^2+28*q^2 are prime },

E(4) = {1,3,5,7,9,11,13,15} = { 2n-1: A218825(n)=0 },

E(15) = {1,3,5,7,9,13,15,31,33,35,37,73,89,157} = { 2n-1: for no prime q, both p=2n-1-2q and p^2+4(2^15-1)q^2 are prime }.

Cf. A218825, A046927, A000040.

Sequence in context: A107537 A260500 A202644 * A210626 A341553 A340437

Adjacent sequences: A218827 A218828 A218829 * A218831 A218832 A218833

nonn,more

Zhi-Wei Sun and M. F. Hasler, Nov 07 2012

approved