A180263 - OEIS

%I #27 Sep 08 2022 08:45:54

%S 1,7,13,17,21,23,27,31,33,37,41,43,47,53,55,57,63,67,73,75,77,81,83,

%T 87,89,91,93,97,99,103,105,107,109,111,113,115,117,119,123,125,127,

%U 129,133,135,137,143,147,149,151,153,155,157,161,163,167,173,177,179,183,185

%N Odd k such that (k^2 + 1)/2 is not prime.

%H Harvey P. Dale, <a href="/A180263/b180263.txt">Table of n, a(n) for n = 1..2000</a>

%e a(2)=7: (7^2 + 1)/2 = 25, which is not prime, so 7 is in the sequence.

%e (9^2 + 1)/2 = 41, which is prime, so 9 is not in the sequence.

%t a={};For[i=1,i<100,i=i+2,If[PrimeQ[(i^2+1)/2],0,AppendTo[a,i]]]Print[a]

%t Select[Range[1,201,2],!PrimeQ[(#^2+1)/2]&] (* _Harvey P. Dale_, Jan 07 2016 *)

%o (Magma) [ n: n in [1..200 by 2] | not IsPrime((n^2+1) div 2) ];

%o (PARI) isok(n) = (n%2) && !isprime((n^2 + 1)/2); \\ _Michel Marcus_, Nov 23 2018

%Y Cf. A027862 (primes of the form (n^2+1)/2).

%K nonn

%O 1,2

%A _Alex Meiburg_, Aug 21 2010

%E More terms from _Vincenzo Librandi_, Nov 18 2010

%E Example clarified by _Harvey P. Dale_, Jan 07 2016