A229139 Smallest m such that Fibonacci(2n-1) = m^2 + k^2.
0, 1, 1, 2, 3, 5, 8, 9, 21, 34, 55, 89, 73, 13, 377, 610, 987, 64, 244, 4155, 4554, 10946, 2191, 28657, 15857, 74957, 34022, 29811, 50481, 134104, 832040, 162589, 387938, 711703, 1556305, 6229800, 4173137, 4059539, 1972951, 51797450, 4866315, 165580141, 46049477, 202620393, 348451533, 181781990
Offset: 1
Keywords
Examples
A000045(2*6-1) = 89 = 5^2 + 8^2 so a(6)=5. A000045(2*8-1) = 610 = 9^2 + 23^2 = 13^2 + 21^2, so a(8)=9.
Programs
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Haskell
a229139 1 = 0 a229139 n = head $ dropWhile (== 0) $ map (a037213 . (t -) . (^ 2)) [s, s - 1 ..] where t = a000045 (2 * n - 1); s = a000196 t -- Reinhard Zumkeller, Oct 11 2013
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PARI
for(n=1, 10^6, t=fibonacci(2*n-1);s=sqrtint(t);forstep(i=s,1,-1,if(issquare(t-i*i),print1(sqrtint(t-i*i), ",");break)))
Comments