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%I #49 Jun 28 2024 03:22:47
%S 0,1,67653,2124804
%N Numbers k such that 2*k^2 + 1 divides 2^k + 1.
%C Numbers k such that (2^k + 1)/(2*k^2 + 1) is an integer.
%C a(5) > 2*10^10. - _Chai Wah Wu_, Dec 07 2014
%t a247221[n_Integer] := Select[Range[n], Divisible[2^# + 1, 2*#^2 + 1] &]; a247221[2500000] (* _Michael De Vlieger_, Nov 30 2014 *)
%o (Magma) [n: n in [1..300000] | Denominator((2^n+1)/(2*n^2+1)) eq 1];
%o (PARI) for(n=0,10^9,if(Mod(2,2*n^2+1)^n==-1,print1(n,", "))); \\ _Joerg Arndt_, Nov 30 2014
%o (Python)
%o A247221_list = [n for n in range(10**6) if pow(2,n,2*n*n+1) == 2*n*n]
%o # _Chai Wah Wu_, Dec 07 2014
%Y Cf. A247205, A247220.
%K nonn,more
%O 1,3
%A _Juri-Stepan Gerasimov_, Nov 30 2014