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A134406 Composite numbers of the form n^2 + 1. 16
10, 26, 50, 65, 82, 122, 145, 170, 226, 290, 325, 362, 442, 485, 530, 626, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1370, 1445, 1522, 1682, 1765, 1850, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 3026, 3250, 3365, 3482, 3601, 3722 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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(50) = [7;{2,7}], ..., where {} is denoted a period (we write {6} == {2,3}).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=10 because 10 = 3^2 + 1 is composite,

a(2)=26 because 26 = 5^2 + 1 is composite,

a(3)=50 because 50 = 7^2 + 1 is composite.

MAPLE

ts_fn1:=proc(n) local i, tren, ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false) then ans:=[ op(ans), tren ]: fi od: RETURN(ans) end: ts_fn1(200);

MATHEMATICA

Select[Range[70]^2+1, !PrimeQ[#]&] (* Harvey P. Dale, Aug 12 2012 *)

PROG

(PARI) for(n=3, 99, if(!isprime(t=n^2+1), print1(t", "))) \\ Charles R Greathouse IV, Aug 29 2016

CROSSREFS

Cf. A002496, A005574.

Sequence in context: A044452 A198017 A137351 * A099978 A242719 A242489

Adjacent sequences:  A134403 A134404 A134405 * A134407 A134408 A134409

KEYWORD

nonn

AUTHOR

Jani Melik, Jan 18 2008

STATUS

approved

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Last modified July 21 12:41 EDT 2017. Contains 289642 sequences.