A091113 - OEIS

%I #27 Sep 22 2025 16:00:43

%S 1,9,21,25,33,45,49,57,65,69,77,81,85,93,105,117,121,125,129,133,141,

%T 145,153,161,165,169,177,185,189,201,205,209,213,217,221,225,237,245,

%U 249,253,261,265,273,285,289,297,301,305,309,321,325,329,333,341,345

%N Nonprimes of the form 4*k+1.

%C A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - _Antti Karttunen_, Jul 02 2024

%H Muniru A Asiru, <a href="/A091113/b091113.txt">Table of n, a(n) for n = 1..10000</a>

%p A091113 := proc(n)

%p     option remember;

%p     if n =1 then

%p         1;

%p     else

%p         for a from procname(n-1)+4 by 4 do

%p             if not isprime(a) then

%p                 return a;

%p             end if;

%p         end do:

%p     end if;

%p end proc:

%p seq(A091113(n),n=1..100) ; # _R. J. Mathar_, Aug 29 2018

%t Do[If[ !PrimeQ[n]&&Equal[Mod[n, 4], 1], Print[n]], {n, 1, 1000}]

%t Select[4*Range[0,100]+1,!PrimeQ[#]&] (* _Harvey P. Dale_, Oct 28 2017 *)

%o (GAP) Filtered(List([0..100],k->4*k+1),n->not IsPrime(n)); # _Muniru A Asiru_, Mar 10 2019

%o (Magma) [n: n in [1..350] | IsIntegral((n-1)/4) and not IsPrime(n)]; // _G. C. Greubel_, Mar 10 2019

%o (SageMath) [n for n in (1..350) if ((n-1)/4).is_integer() and not is_prime(n)] # _G. C. Greubel_, Mar 10 2019

%o (PARI) isok(n) = !isprime(n) && !((n-1) % 4); \\ _Michel Marcus_, Mar 11 2019

%Y Cf. A014076, A091236, A373978 (characteristic function).

%Y Subsequence of A016813 (4*n+1).

%Y Cf. also A291745.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 24 2004