A319216 Numbers k such that k^2 + 1 divides 2^k + 2.

0, 1, 3, 15, 79, 511, 4095, 6735, 65535, 2097151, 16777215, 75955411, 68719476735, 137438953471

Offset

1,3

Comments

Numbers t such that 2^t-1 is a term are 0, 1, 2, 4, 9, 12, 16, 21, ...

Primes p such that 2^((p^2-1)/2)-1 is a term are 3, 5, 7, 13, 19, 29, 37, 43, 47, 61, 71, 89, 103, 107, 127, 131, 139, 173, 191, 211, ...(cf. A062326).

a(14) > 10^11. - Hiroaki Yamanouchi, Sep 14 2018

Links

Table of n, a(n) for n=1..14.

Prog

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

Crossrefs

Cf. A015921, A062326, A097958, A244673, A247220.

Sequence in context: A052755 A137957 A002514 * A093889 A369085 A020044

Adjacent sequences: A319213 A319214 A319215 * A319217 A319218 A319219

Keyword

nonn,more

Author

Altug Alkan, Sep 13 2018, following a suggestion from Max Alekseyev

Extensions

a(13) from Hiroaki Yamanouchi, Sep 14 2018

a(14) from Giovanni Resta, Sep 17 2018

Status

approved