A002333 Numbers y such that p = x^2 + 2y^2, with prime p = A033203(n). (Formerly M0444 N0166)

1, 1, 1, 2, 3, 4, 3, 5, 3, 6, 1, 2, 6, 7, 4, 5, 8, 3, 9, 7, 6, 9, 1, 2, 6, 11, 4, 10, 9, 3, 12, 9, 12, 13, 8, 3, 14, 12, 13, 6, 1, 2, 12, 11, 5, 15, 16, 9, 3, 13, 8, 15, 12, 17, 16, 6, 14, 15, 10, 3, 17, 18, 11, 9, 15, 4, 18, 9, 20, 15, 7, 8, 3, 20, 21, 21, 10, 18, 19, 16, 11, 22, 18

Offset

1,4

Comments

The corresponding x numbers are given in A002332.

References

A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904. [Annotated scans of selected pages]

D. S., Review of A Table of Primes of Z[(-2)^(1/2)] by J. H. Jordan and J. R. Rabung, Math. Comp., 23 (1969), p. 458.

Mathematica

g[p_] := For[y=1, True, y++, If[IntegerQ[Sqrt[p-2y y]], Return[y]]]; g/@Select[Prime/@Range[1, 200], Mod[ #, 8]<4&]

Crossrefs

Cf. A002332.

Sequence in context: A322816 A323078 A331301 * A323241 A322311 A323237

Adjacent sequences: A002330 A002331 A002332 * A002334 A002335 A002336

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Dean Hickerson, Oct 07 2001

Status

approved