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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) 23
 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 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 Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) A. T. Benjamin and D. Zeilberger, Pythagorean primes and palindromic continued fractionsINTEGERS 5(1) (2005) #A30 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 a(n+1) = Min(A002972(n), 2*A002973(n)). - Reinhard Zumkeller, Feb 16 2010 a(n) = A363051(A002313(n)). - R. J. Mathar, Jan 31 2024 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. # alternative A002331 := proc(n) A363051(A002313(n)) ; end proc: seq(A002331(n), n=1..100) ; # R. J. Mathar, Feb 01 2024 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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Last modified April 20 07:26 EDT 2024. Contains 371799 sequences. (Running on oeis4.)