A327636 Numbers k such that 2k + 1 divides 2^k + k^2.

0, 1, 313, 30853, 42992, 247753, 584989, 4130748, 4390945, 4780473, 5871073, 7615813, 8123113, 13514233, 13971013, 19128653, 19392433, 43794833, 51644173, 67314973, 69522073, 108168073, 124498753, 124510153, 177694105, 198750308, 208302253, 212791885, 230815033

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 20 2019

Keywords

• nonn

Comments

2*a(n) + 1: 1, 3, 627, 61707, 85985, 495507, 1169979, 8261497, ...

Crossrefs

Cf. A001580, A242776.

Programs

Magma

[n: n in [0..100000] | Denominator((2^n+n^2)/(2*n+1)) eq 1];

Mathematica

Do[ k=2*n+1; f=PowerMod[ 2, n, k ] + PowerMod[ n, 2, k ]; If[ IntegerQ[ f/k ], Print[ n ] ], {n, 0, 10^7} ] (* Metin Sariyar, Sep 21 2019 *)

PARI

is(n) = Mod(2, 2*n+1)^n==-n^2 \\ Felix Fröhlich, Sep 20 2019

Extensions

More terms from Felix Fröhlich, Sep 20 2019

Offset 1 from Michel Marcus, Jul 02 2021