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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

(PARI) ispow2(n)=n>0 && n==1<<valuation(n, 2)
is(n)=!ispow2(lift(Mod(2, n)^n))

Crossrefs

Cf. A015910, A015911.

Sequence in context: A127066 A331382 A154362 * A072462 A369951 A088827

Adjacent sequences: A226218 A226219 A226220 * A226222 A226223 A226224

Keyword

nonn

Author

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

Status

approved