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Numbers n such that n^2 + 1 is composite.
8

%I #12 Sep 15 2014 14:12:04

%S 3,5,7,8,9,11,12,13,15,17,18,19,21,22,23,25,27,28,29,30,31,32,33,34,

%T 35,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,55,57,58,59,60,61,

%U 62,63,64,65,67,68,69,70,71,72,73,75,76,77,78,79,80,81,82,83,85,86,87,88

%N Numbers n such that n^2 + 1 is composite.

%F a(n) ~ n. - _Charles R Greathouse IV_, Sep 15 2014

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

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

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

%p ts_fn2:=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), i ]: fi od: RETURN(ans) end: ts_fn2(200);

%t Select[Range@100,!PrimeQ[#^2+1]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012 *)

%o (PARI) is(n)=!isprime(n^2+1) \\ _Charles R Greathouse IV_, Sep 15 2014

%Y Cf. A002496, A002808, A005574, A018252.

%K nonn,easy

%O 1,1

%A _Jani Melik_, Jan 18 2008