A002332 Numbers x such that p = x^2 + 2y^2, with prime p = A033203(n). (Formerly M2264 N0894)

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

1,3

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.

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& ]

Crossrefs

Cf. A002333.

Sequence in context: A080094 A201873 A317931 * A332547 A302694 A245668

Adjacent sequences: A002329 A002330 A002331 * A002333 A002334 A002335

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Dean Hickerson, Oct 07 2001

Status

approved