A002332 Numbers x such that p = x^2 + 2y^2, with prime p = A033203(n).

0, 1, 3, 3, 1, 3, 5, 3, 7, 1, 9, 9, 5, 3, 9, 9, 3, 11, 1, 9, 11, 7, 15, 15, 13, 3, 15, 9, 11, 17, 5, 13, 7, 3, 15, 19, 3, 11, 9, 19, 21, 21, 13, 15, 21, 7, 3, 19, 23, 15, 21, 11, 17, 3, 9, 23, 15, 13, 21, 25, 9, 5, 21, 23, 17, 27, 11, 25, 3, 19, 27, 27, 29, 9, 1, 5, 27, 17, 15, 21, 27

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

For p>2, x and y are uniquely determined [Frei, Th. 3]. - N. J. A. Sloane, May 30 2014

The corresponding y numbers are given in A002333.

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]
• G. Frei, Euler's convenient numbers, Math. Intell. Vol. 7 No. 3 (1985), 55-58 and 64.
• 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. A002333.

Programs

Mathematica

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

Extensions

More terms from Dean Hickerson, Oct 07 2001