A218830 Largest odd integer not of the form p+2q with p, q, p^2+4(2^n-1)q^2 all prime, or 0 if there would be no such upper bound.

3449, 1711, 73, 15, 6227, 1051, 2239, 2599, 7723, 781, 1163, 587, 11443, 2279, 157, 587, 32041, 1051, 2083, 4681

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

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.

Examples

			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 }.
		

Links

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

Crossrefs

Cf. A218825, A046927, A000040.