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

%I M2264 N0894

%S 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,

%T 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,

%U 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

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

%C For p>2, x and y are uniquely determined [Frei, Th. 3]. - _N. J. A. Sloane_, May 30 2014

%C The corresponding y numbers are given in A002333.

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

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

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

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

%H T. D. Noe, <a href="/A002332/b002332.txt">Table of n, a(n) for n = 1..1000</a>

%H A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904. [Annotated scans of selected pages]

%H G. Frei, <a href="https://doi.org/10.1007/BF03025809">Euler's convenient numbers</a>, Math. Intell. Vol. 7 No. 3 (1985), 55-58 and 64.

%H D. S., <a href="https://doi.org/10.1090/S0025-5718-69-99644-6">Review of A Table of Primes of Z[(-2)^(1/2)] by J. H. Jordan and J. R. Rabung</a>, Math. Comp., 23 (1969), p. 458.

%t 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& ]

%Y Cf. A002333.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Dean Hickerson_, Oct 07 2001

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)