A091113 Nonprimes of the form 4*k+1.

1, 9, 21, 25, 33, 45, 49, 57, 65, 69, 77, 81, 85, 93, 105, 117, 121, 125, 129, 133, 141, 145, 153, 161, 165, 169, 177, 185, 189, 201, 205, 209, 213, 217, 221, 225, 237, 245, 249, 253, 261, 265, 273, 285, 289, 297, 301, 305, 309, 321, 325, 329, 333, 341, 345

Offset: 1

Author

Labos Elemer, Feb 24 2004

Keywords

• nonn

Comments

A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - Antti Karttunen, Jul 02 2024

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000

Crossrefs

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

Subsequence of A016813 (4*n+1).

Cf. also A291745.

Programs

GAP

Filtered(List([0..100],k->4*k+1),n->not IsPrime(n)); # Muniru A Asiru, Mar 10 2019

Magma

[n: n in [1..350] | IsIntegral((n-1)/4) and not IsPrime(n)]; // G. C. Greubel, Mar 10 2019

Maple

A091113 := proc(n)
    option remember;
    if n =1 then
        1;
    else
        for a from procname(n-1)+4 by 4 do
            if not isprime(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A091113(n),n=1..100) ; # R. J. Mathar, Aug 29 2018

Mathematica

Do[If[ !PrimeQ[n]&&Equal[Mod[n, 4], 1], Print[n]], {n, 1, 1000}]
Select[4*Range[0,100]+1,!PrimeQ[#]&] (* Harvey P. Dale, Oct 28 2017 *)

PARI

isok(n) = !isprime(n) && !((n-1) % 4); \\ Michel Marcus, Mar 11 2019

Sage

[n for n in (1..350) if ((n-1)/4).is_integer() and not is_prime(n)] # G. C. Greubel, Mar 10 2019