A226221 Numbers n such that 2^n mod n is not a power of 2.

1, 2, 4, 8, 16, 18, 25, 27, 32, 35, 36, 42, 45, 49, 50, 54, 55, 64, 70, 75, 77, 81, 88, 91, 95, 98, 99, 100, 104, 105, 108, 110, 115, 117, 119, 121, 125, 128, 130, 135, 136, 140, 143, 147, 150, 152, 153, 155, 156, 160, 161, 162, 169, 171, 175, 180, 184, 187, 189, 190, 198, 200

Offset: 1

Author

J. M. Bergot and Charles R Greathouse IV, May 31 2013

Keywords

• nonn

Comments

All terms beyond the first two are composite: this is a subsequence of A065090.

Examples

			2^18 = 262144 = 10 mod 18 and 10 is not a power of 2, so 18 is in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A015910, A015911.

Programs

Maple

isA226221 := proc(n)
    local m ;
    if n <= 2 then
        return true;
    end if;
    m := A015910(n) ;
    if type(m,'odd') or m = 0 then
        true;
    elif nops(numtheory[factorset](m))  >1 then
        true;
    else
        false;
    end if;
end proc:
A226221 := proc(n)
    local a;
    if n <= 2 then
        n;
    else
        for a from procname(n-1)+1 do
            if isA226221(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A226221(n),n=1..30) ; # R. J. Mathar, Jun 06 2013

Mathematica

Select[Range[200],!IntegerQ[Log[2,PowerMod[2,#,#]]]&] (* Harvey P. Dale, Feb 28 2022 *)

PARI

ispow2(n)=n>0 && n==1<