Search: id:A134406
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%I A134406
%S A134406 10,26,50,65,82,122,145,170,226,290,325,362,442,485,530,626,730,785,842,
%T A134406 901,962,1025,1090,1157,1226,1370,1445,1522,1682,1765,1850,1937,2026,
%U A134406 2117,2210,2305,2402,2501,2602,2705,2810,3026,3250,3365,3482,3601,3722
%N A134406 Composite numbers of the form n^2 + 1.
%C A134406 Square roots of these numbers are quadratic irrationals and corresponding 
               chain fraction reresentations 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}).
%e A134406 a(1)=10 because 10 = 3^2 + 1 is a composite number,
%e A134406 a(2)=26 because 26 = 5^2 + 1 is a composite number,
%e A134406 a(3)=50 becasue 50 = 7^2 + 1 is composite.
%p A134406 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);
%Y A134406 Cf. A002496, A005574.
%Y A134406 Sequence in context: A113770 A044452 A137351 this_sequence A099978 A074789 
               A125075
%Y A134406 Adjacent sequences: A134403 A134404 A134405 this_sequence A134407 A134408 
               A134409
%K A134406 nonn
%O A134406 1,1
%A A134406 Jani Melik (jani_melik(AT)hotmail.com), Jan 18 2008

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