A192579 Primes p for which there is no prime q == 3 (mod 4) that is smaller than p and is a quadratic residue modulo p.

2, 3, 5, 7, 17

Offset

1,1

Comments

Gica proved that if p is a prime different from 2, 3, 5, 7, 17, then there exists a prime q < p which is a quadratic residue modulo p and q == 3 (mod 4).

This is the unique set of primes answering the question in the Mathematics Stack Exchange link. - Rick L. Shepherd, May 29 2016

Links

Table of n, a(n) for n=1..5.

A. Gica, Quadratic residues of certain types, Rocky Mt. J. Math. 36 (2006), 1867-1871.

A. Gica, Quadratic residues of certain types, Journées Arithmétiques 2011.

Mathematics Stack Exchange, x, y, x - y and x + y are prime numbers. What is their sum?

Example

p = 17 is a member, because the primes q < p with q == 3 (mod 4) are q = 3, 7, 11, and they are not quadratic residues modulo 17.
11 is not a member, because 3 < 11 and 3 == 5^2 (mod 11).

Crossrefs

Cf. A192578.

Sequence in context: A094575 A145968 A343537 * A215658 A295266 A059471

Adjacent sequences: A192576 A192577 A192578 * A192580 A192581 A192582

Keyword

nonn,fini,full

Author

Jonathan Sondow, Jul 04 2011

Status

approved