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Numbers y such that p = x^2 + 2y^2, with prime p = A033203(n).
(Formerly M0444 N0166)
4

%I M0444 N0166 #27 Jul 14 2019 08:12:24

%S 1,1,1,2,3,4,3,5,3,6,1,2,6,7,4,5,8,3,9,7,6,9,1,2,6,11,4,10,9,3,12,9,

%T 12,13,8,3,14,12,13,6,1,2,12,11,5,15,16,9,3,13,8,15,12,17,16,6,14,15,

%U 10,3,17,18,11,9,15,4,18,9,20,15,7,8,3,20,21,21,10,18,19,16,11,22,18

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

%C The corresponding x numbers are given in A002332.

%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="/A002333/b002333.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 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 g[p_] := For[y=1, True, y++, If[IntegerQ[Sqrt[p-2y y]], Return[y]]]; g/@Select[Prime/@Range[1, 200], Mod[ #, 8]<4&]

%Y Cf. A002332.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E More terms from _Dean Hickerson_, Oct 07 2001