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

%I A002332 M2264 N0894 #30 Jul 14 2019 11:01:24
%S A002332 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 A002332 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 A002332 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 A002332 Numbers x such that p = x^2 + 2y^2, with prime p = A033203(n).
%C A002332 For p>2, x and y are uniquely determined [Frei, Th. 3]. - _N. J. A. Sloane_, May 30 2014
%C A002332 The corresponding y numbers are given in A002333.
%D A002332 A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
%D A002332 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
%D A002332 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002332 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002332 T. D. Noe, <a href="/A002332/b002332.txt">Table of n, a(n) for n = 1..1000</a>
%H A002332 A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904. [Annotated scans of selected pages]
%H A002332 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 A002332 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 A002332 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 A002332 Cf. A002333.
%K A002332 nonn
%O A002332 1,3
%A A002332 _N. J. A. Sloane_
%E A002332 More terms from _Dean Hickerson_, Oct 07 2001