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 A002330 Value of y in the solution to p = x^2 + y^2, x <= y, with prime p = A002313(n). (Formerly M0462 N0169) 39
 1, 2, 3, 4, 5, 6, 5, 7, 6, 8, 8, 9, 10, 10, 8, 11, 10, 11, 13, 10, 12, 14, 15, 13, 15, 16, 13, 14, 16, 17, 13, 14, 16, 18, 17, 18, 17, 19, 20, 20, 15, 17, 20, 21, 19, 22, 20, 21, 19, 20, 24, 23, 24, 18, 19, 25, 22, 25, 23, 26, 26, 22, 27, 26, 20, 25, 22, 26, 28, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals A096029(n) + A096030(n) + 1, for entries after the first. - Lekraj Beedassy, Jul 21 2004 a(n+1) = MAX(A002972(n), 2*A002973(n)). [From 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 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 a := []; for x from 0 to 50 do for y from x to 50 do p := x^2+y^2; if isprime(p) then a := [op(a), [p, x, y]]; fi; od: od: writeto(trans); for i from 1 to 158 do lprint(a[i]); od: # then sort the triples in "trans" MATHEMATICA Flatten[#, 1]&[Table[PowersRepresentations[Prime[k], 2, 2], {k, 1, 142}]][[All, 2]] (* Jean-François Alcover, Jul 05 2011 *) PROG (PARI) f(p)=my(s=lift(sqrt(Mod(-1, p))), x=p, t); if(s>p/2, s=p-s); while(s^2>p, t=s; s=x%s; x=t); s forprime(p=2, 1e3, if(p%4-3, print1(f(p)", "))) \\ Charles R Greathouse IV, Apr 24 2012 (PARI) do(p)=qfbsolve(Qfb(1, 0, 1), p)[1] forprime(p=2, 1e3, if(p%4-3, print1(do(p)", "))) \\ Charles R Greathouse IV, Sep 26 2013 CROSSREFS Cf. A002331, A002313, A002144. Sequence in context: A245352 A099033 A187786 * A305900 A287943 A305211 Adjacent sequences:  A002327 A002328 A002329 * A002331 A002332 A002333 KEYWORD nonn AUTHOR STATUS approved

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Last modified February 18 03:44 EST 2020. Contains 332006 sequences. (Running on oeis4.)