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.

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A134420 Composite squarefree numbers of the form k^2 + 1.

Original entry on oeis.org

10, 26, 65, 82, 122, 145, 170, 226, 290, 362, 442, 485, 530, 626, 730, 785, 842, 901, 962, 1090, 1157, 1226, 1370, 1522, 1765, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 3026, 3365, 3482, 3601, 3722, 3845, 3970, 4097, 4226, 4490, 4762
Offset: 1

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Author

Jani Melik, Jan 18 2008

Keywords

Comments

Square roots of these numbers are quadratic irrationals and corresponding chain fraction representations are periodic: sqrt(10) = [3;{2,3}], sqrt(26) = [5;{2,5}], sqrt(65) = [8;{2,8}], ..., where {} is denoted a period (we write {6} == {2,3}).

Examples

			a(1)=10 because 10 = 3^2 + 1 is squarefree.
a(2)=26 because 26 = 5^2 + 1 is squarefree.
a(3)=65 because 65 = 8^2 + 1 is squarefree.
		

Crossrefs

Programs

  • Maple
    ts_fn3:=proc(n) local i,tren,ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false and numtheory[mobius] (tren) <> 0 ) then ans:=[ op(ans), tren ]: fi od: RETURN(ans) end: ts_fn3(200);
  • Mathematica
    Select[Range[70]^2+1, CompositeQ[#] && SquareFreeQ[#] &] (* Amiram Eldar, Feb 22 2021 *)

Formula

a(n) = A002522(A134427(n)). - Amiram Eldar, Feb 22 2021

Extensions

Definition corrected by T. D. Noe, Sep 16 2008
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