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A188983 Odd numbers y such that x^2 + y^2 = 13^n with x and y coprime. 3

%I

%S 1,3,5,9,119,597,2035,4449,239,56403,341525,1315911,3455641,3627003,

%T 23161315,186118929,815616479,2474152797,4241902555,6712571031,

%U 95420159401,485257533003,1671083125805,3718150825791,584824319281,44827014819597,276564805068235,1076637637754649,2864483360640839,3190610873034597,18094618450123325

%N Odd numbers y such that x^2 + y^2 = 13^n with x and y coprime.

%C The x values are in A188982.

%C This is also the absolute value of the real part of (3+2i)^n, where i = sqrt(-1). The signed version is A121622.

%H Vincenzo Librandi, <a href="/A188983/b188983.txt">Table of n, a(n) for n = 0..183</a>

%t Table[s = Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &, 1][[1]]; Select[s, OddQ][[1]], {n, 0, 30}]

%o (MAGMA) [Integers()!Abs(Real((3+2*Sqrt(-1))^n)): n in [0..30]]; // [See comment by T.D. Noe.] Bruno Berselli, May 26 2011

%Y Cf. A158936, A188982.

%K nonn

%O 0,2

%A _T. D. Noe_, Apr 14 2011

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)