A319222 Numbers k such that k divides 2^(2k+1) + 1.

1, 3, 129, 2537, 51889, 101617, 226873, 270427, 653467, 945667, 1740979, 5819937, 6520987, 9828587, 15452867, 24950857, 51377539, 89519449, 108627601, 135776371, 160126609, 296338873, 310026163, 400431289, 641706243, 643359937, 678257563, 803419697, 902661523, 952431331, 1004273987, 1243893697, 1796055907

Offset

1,2

Comments

Also, numbers k such that 4^k == -1/2 (mod k) (cf. A296369). - Max Alekseyev, Sep 15 2018

If k is in the sequence, and m is another divisor of 2^(2*k+1)+1 and is coprime to k, then m*k is in the sequence. - Robert Israel, Sep 14 2018

Links

Table of n, a(n) for n=1..33.

Maple

filter:= n -> 2 &^ (2*n+1)+1 mod n = 0:
select(filter, [$1..10^7]); # Robert Israel, Sep 14 2018

Prog

(PARI) is_A319222(n) = Mod(2, n)^(2*n+1)==-1;

Crossrefs

Cf. A006517, A006521, A015950.

Sequence in context: A243213 A264582 A108713 * A300543 A300970 A300927

Adjacent sequences: A319219 A319220 A319221 * A319223 A319224 A319225

Keyword

nonn

Author

Altug Alkan, Sep 13 2018

Status

approved