A091968 Primes congruent to 3 (mod 16).

3, 19, 67, 83, 131, 163, 179, 211, 227, 307, 419, 467, 499, 547, 563, 643, 659, 691, 739, 787, 883, 947, 1091, 1123, 1171, 1187, 1283, 1427, 1459, 1523, 1571, 1619, 1667, 1699, 1747, 1811, 1907, 1987, 2003, 2083, 2099, 2131, 2179, 2243, 2339, 2371, 2467

Offset

1,1

Comments

For any n, the equations x^4 - y^4 = a(n)*z^2 and x^4 - a(n)^2*y^4 = z^2 are not solvable in natural numbers. - Arkadiusz Wesolowski, Aug 15 2013

References

L. J. Mordell, Diophantine Equations, Ac. Press, p. 23.

Trygve Nagell, Introduction to Number Theory, Chelsea Publishing Company, NY, 1964, p. 230.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Mathematica

Select[Prime@Range[400], Mod[ #, 16] == 3 &] (* Ray Chandler, Dec 06 2006 *)

Prog

(PARI) is(n)=isprime(n) && n%16==3 \\ Charles R Greathouse IV, Jul 01 2016

Crossrefs

Cf. A092022, A093012.

Sequence in context: A178747 A071245 A297744 * A351859 A158714 A064056

Adjacent sequences: A091965 A091966 A091967 * A091969 A091970 A091971

Keyword

nonn,easy

Author

Giovanni Teofilatto, Mar 14 2004

Extensions

More terms from Ray Chandler, Mar 15 2004

Status

approved