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

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A002332.

Programs

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&]

Extensions

More terms from Dean Hickerson, Oct 07 2001