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 A002331 Values of x in the solution to p = x^2 + y^2, x <= y, with prime p = A002313(n). (Formerly M0096 N0033) 22
 1, 1, 2, 1, 2, 1, 4, 2, 5, 3, 5, 4, 1, 3, 7, 4, 7, 6, 2, 9, 7, 1, 2, 8, 4, 1, 10, 9, 5, 2, 12, 11, 9, 5, 8, 7, 10, 6, 1, 3, 14, 12, 7, 4, 10, 5, 11, 10, 14, 13, 1, 8, 5, 17, 16, 4, 13, 6, 12, 1, 5, 15, 2, 9, 19, 12, 17, 11, 5, 14, 10, 18, 4, 6, 16, 20, 19, 10, 13, 4, 6, 15, 22, 11, 3, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n+1) = MIN(A002972(n), 2*A002973(n)). [Reinhard Zumkeller, Feb 16 2010] REFERENCES A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1. 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 and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Noe) John Brillhart, Note on representing a prime as a sum of two squares, Math. Comp. 26 (1972), pp. 1011-1013. A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904 [Annotated scans of selected pages] K. Matthews, Serret's algorithm Server J. Todd, A problem on arc tangent relations, Amer. Math. Monthly, 56 (1949), 517-528. Eric Weisstein's World of Mathematics, Fermat's 4n Plus 1 Theorem FORMULA a(n) = A096029(n) - A096030(n) for n>1. - Lekraj Beedassy, Jul 16 2004 EXAMPLE The following table shows the relationship between several closely related sequences: Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b; a = A002331, b = A002330, t_1 = ab/2 = A070151; p^2 = c^2+d^2 with c < d; c = A002366, d = A002365, t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079, with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2). --------------------------------- .p..a..b..t_1..c...d.t_2.t_3..t_4 --------------------------------- .5..1..2...1...3...4...4...3....6 13..2..3...3...5..12..12...5...30 17..1..4...2...8..15...8..15...60 29..2..5...5..20..21..20..21..210 37..1..6...3..12..35..12..35..210 41..4..5..10...9..40..40...9..180 53..2..7...7..28..45..28..45..630 ................................. MAPLE See A002330 for Maple program. MATHEMATICA pmax = 1000; x[p_] := Module[{x, y}, x /. ToRules[Reduce[0 <= x <= y && x^2 + y^2 == p, {x, y}, Integers]]]; For[n=1; p=2, p

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