Search: id:A002330
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%I A002330 M0462 N0169
%S A002330 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,
%T A002330 13,14,16,17,13,14,16,18,17,18,17,19,20,20,15,17,20,21,19,22,20,21,
%U A002330 19,20,24,23,24,18,19,25,22,25,23,26,26,22,27,26,20,25,22,26,28,25
%N A002330 Value of y in the solution to p = x^2 + y^2, x <= y, with prime p = A002313(n).
%C A002330 Equals A096029(n) + A096030(n) + 1, for entries after the first. - Lekraj 
               Beedassy (blekraj(AT)yahoo.com), Jul 21 2004
%D A002330 A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 
               1.
%D A002330 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002330 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002330 J. Todd, A problem on arc tangent relations, Amer. Math. Monthly, 56 
               (1949), 517-528.
%H A002330 T. D. Noe, <a href="b002330.txt">Table of n, a(n) for n=1..1000</a>
%H A002330 K. Matthews, <a href="http://www.numbertheory.org/php/serret.html">Serret's 
               algorithm Server</a>
%H A002330 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Fermats4nPlus1Theorem.html">Fermat's 4n Plus 1 Theorem</a>
%e A002330 The following table shows the relationship
%e A002330 between several closely related sequences:
%e A002330 Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;
%e A002330 a = A002331, b = A002330, t_1 = ab/2 = A070151;
%e A002330 p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,
%e A002330 t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,
%e A002330 with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).
%e A002330 ---------------------------------
%e A002330 .p..a..b..t_1..c...d.t_2.t_3..t_4
%e A002330 ---------------------------------
%e A002330 .5..1..2...1...3...4...4...3....6
%e A002330 13..2..3...3...5..12..12...5...30
%e A002330 17..1..4...2...8..15...8..15...60
%e A002330 29..2..5...5..20..21..20..21..210
%e A002330 37..1..6...3..12..35..12..35..210
%e A002330 41..4..5..10...9..40..40...9..180
%e A002330 53..2..7...7..28..45..28..45..630
%e A002330 .................................
%p A002330 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"
%Y A002330 Cf. A002331, A002313, A002144.
%Y A002330 Sequence in context: A102730 A165597 A099033 this_sequence A091951 A063283 
               A036055
%Y A002330 Adjacent sequences: A002327 A002328 A002329 this_sequence A002331 A002332 
               A002333
%K A002330 nonn,easy
%O A002330 1,2
%A A002330 N. J. A. Sloane (njas(AT)research.att.com).

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