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

1,1

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.

Links

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.

Example

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 }.

Crossrefs

Cf. A218825, A046927, A000040.

Sequence in context: A107537 A260500 A202644 * A210626 A341553 A340437

Adjacent sequences: A218827 A218828 A218829 * A218831 A218832 A218833

Keyword

nonn,more

Author

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

Status

approved