A078116 Primes of the form x^2 + 2y^2 where y<=x. Terms are listed in increasing order of x; for fixed x they're in increasing order of y.

3, 11, 17, 43, 67, 83, 89, 113, 131, 179, 139, 193, 283, 241, 331, 457, 227, 233, 257, 353, 467, 563, 617, 307, 577, 739, 379, 433, 523, 811, 1009, 443, 449, 491, 569, 641, 683, 953, 1019, 1163, 547, 601, 691, 643, 787, 1777, 761, 827, 857, 929, 971, 1307

Offset

1,1

Comments

Every prime of the form 8n+1 or 8n+3 has a unique representation of the form x^2 + 2y^2 with positive integers x and y. This sequence has the primes for which y<=x.

References

Morris Kline, Mathematical Thought From Ancient to Modern Times, Oxford University Press 1972, p. 276 (Fermat prime number theorems).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Mathematica

Select[Flatten[Table[x^2+2y^2, {x, 0, 30}, {y, 0, x}]], PrimeQ]

Prog

(PARI) sqplus2sq(n, m) = ct=0; for(x=1, n, for(y=1, x, s = x^2+m*y^2; if(isprime(s), ct+=1; print1(s" "); ); ); ); \\ Lists primes of the form x^2+m*y^2 with 1<=y<=x<=n.

Crossrefs

Sequence in context: A270225 A262275 A176804 * A245045 A127996 A032008

Adjacent sequences: A078113 A078114 A078115 * A078117 A078118 A078119

Keyword

easy,nonn

Author

Cino Hilliard, Dec 05 2002

Extensions

Edited by Dean Hickerson, Dec 12 2002

Status

approved