A247221 Numbers k such that 2*k^2 + 1 divides 2^k + 1.

0, 1, 67653, 2124804

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 30 2014

Keywords

• nonn
• more

Comments

Numbers k such that (2^k + 1)/(2*k^2 + 1) is an integer.

a(5) > 2*10^10. - Chai Wah Wu, Dec 07 2014

Crossrefs

Cf. A247205, A247220.

Programs

Magma

[n: n in [1..300000] | Denominator((2^n+1)/(2*n^2+1)) eq 1];

Mathematica

a247221[n_Integer] := Select[Range[n], Divisible[2^# + 1, 2*#^2 + 1] &]; a247221[2500000] (* Michael De Vlieger, Nov 30 2014 *)

PARI

for(n=0,10^9,if(Mod(2,2*n^2+1)^n==-1,print1(n,", "))); \\ Joerg Arndt, Nov 30 2014

Python

A247221_list = [n for n in range(10**6) if pow(2,n,2*n*n+1) == 2*n*n]
# Chai Wah Wu, Dec 07 2014