cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A139538 Odd numbers of the form x^2+5y^2 not divisible by 5, with both x and y >== 1.

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%I A139538 #8 Jun 02 2025 00:32:51
%S A139538 9,21,29,41,49,61,69,81,89,101,109,129,141,149,161,181,189,201,229,
%T A139538 241,249,261,269,281,301,309,321,329,349,369,381,389,401,409,421,441,
%U A139538 449,461,469,489,501,509,521,529,541,549,569,581,601,609,621,641,661,669
%N A139538 Odd numbers of the form x^2+5y^2 not divisible by 5, with both x and y >== 1.
%C A139538 All numbers in this sequence are divisible by primes A139513
%D A139538 Dirichlet & Dedekins Lectures on Number Theory (English Translation 1999) p. 119.
%t A139538 a = {}; Do[Do[k = x^2 + 5 y^2; If[OddQ[k], If[Mod[k, 5] != 0, AppendTo[a, k]]], {x, 1, 100}], {y, 1, 100}]; Union[a] (*Artur Jasinski*)
%t A139538 With[{upto=1000},Select[Union[#[[1]]^2+5#[[2]]^2&/@Tuples[Range[Floor[ Sqrt[ upto-5]]],2]],OddQ[#]&&Mod[#,5]!=0&&#<=upto&]] (* _Harvey P. Dale_, Jul 25 2019 *)
%K A139538 nonn
%O A139538 1,1
%A A139538 _Artur Jasinski_, Apr 25 2008, Apr 28 2008
%E A139538 Definition clarified by _Harvey P. Dale_, Jul 25 2019