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A002332
Numbers x such that p = x^2 + 2y^2, with prime p = A033203(n).
(Formerly M2264 N0894)
5
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
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.
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
KEYWORD
nonn
EXTENSIONS
More terms from Dean Hickerson, Oct 07 2001
STATUS
approved