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 A160200 Positive numbers y such that y^2 is of the form x^2+(x+761)^2 with integer x. 3
 541, 761, 1465, 1781, 3805, 8249, 10145, 22069, 48029, 59089, 128609, 279925, 344389, 749585, 1631521, 2007245, 4368901, 9509201, 11699081, 25463821, 55423685, 68187241, 148414025, 323032909, 397424365, 865020329, 1882773769 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (-341, a(1)) and (A122694(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+761)^2 = y^2. lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2). lim_{n -> infinity} a(n)/a(n-1) = (1003+462*sqrt(2))/761 for n mod 3 = {0, 2}. lim_{n -> infinity} a(n)/a(n-1) = (591603+85478*sqrt(2))/761^2 for n mod 3 = 1. LINKS FORMULA a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=541, a(2)=761, a(3)=1465, a(4)=1781, a(5)=3805, a(6)=8249. G.f.: (1-x)*(541+1302*x+2767*x^2+1302*x^3+541*x^4) / (1-6*x^3+x^6). a(3*k-1) = 761*A001653(k) for k >= 1. EXAMPLE (-341, a(1)) = (-341, 541) is a solution: (-341)^2+(-341+761)^2 = 116281+176400 = 292681 = 541^2. (A122694(1), a(2)) = (0, 761) is a solution: 0^2+(0+761)^2 = 579121 = 761^2. (A122694(3), a(4)) = (820, 1781) is a solution: 820^2+(820+761)^2 = 672400+2499561 = 3171961 = 1781^2. PROG (PARI) {forstep(n=-344, 10000000, [3, 1], if(issquare(2*n^2+1522*n+579121, &k), print1(k, ", ")))} CROSSREFS Cf. A122694, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A160201 (decimal expansion of (1003+462*sqrt(2))/761), A160202 (decimal expansion of (591603+85478*sqrt(2))/761^2). Sequence in context: A050960 A142737 A020378 * A112371 A031937 A031921 Adjacent sequences:  A160197 A160198 A160199 * A160201 A160202 A160203 KEYWORD nonn AUTHOR Klaus Brockhaus, May 18 2009 STATUS approved

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Last modified June 18 17:38 EDT 2013. Contains 226355 sequences.