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

1, 3, 5, 9, 119, 597, 2035, 4449, 239, 56403, 341525, 1315911, 3455641, 3627003, 23161315, 186118929, 815616479, 2474152797, 4241902555, 6712571031, 95420159401, 485257533003, 1671083125805, 3718150825791, 584824319281, 44827014819597, 276564805068235, 1076637637754649, 2864483360640839, 3190610873034597, 18094618450123325

Offset

0,2

Comments

The x values are in A188982.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..183

Formula

From Amiram Eldar, Dec 12 2025: (Start)

a(n) = abs(A121622(n)).

a(n) = 13^(n/2) * abs(cos(n * arctan(2/3))). (End)

Mathematica

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

Prog

(Magma) [Integers()!Abs(Real((3+2*Sqrt(-1))^n)): n in [0..30]]; // Bruno Berselli, May 26 2011

Crossrefs

Cf. A121622, A158936, A188982.

Sequence in context: A123220 A098339 A121622 * A083519 A302088 A211414

Adjacent sequences: A188980 A188981 A188982 * A188984 A188985 A188986

Keyword

nonn,easy

Author

T. D. Noe, Apr 14 2011

Status

approved