A224486 Numbers k such that 2*k+1 divides 2^k+1.

1, 2, 5, 6, 9, 14, 18, 21, 26, 29, 30, 33, 41, 50, 53, 54, 65, 69, 74, 78, 81, 86, 89, 90, 98, 105, 113, 114, 125, 134, 138, 141, 146, 153, 158, 165, 173, 174, 186, 189, 194, 198, 209, 210, 221, 230, 233, 245, 249, 254, 261, 270, 273, 278, 281, 285, 293

Offset: 1

Author

Jayanta Basu, Apr 07 2013

Keywords

• nonn

Comments

The numbers are called Curzon numbers by Tattersall (p. 85, exercise 43).

Sequence 2*a(n)+1 apparently is A175865 (certainly it is not A003629). - Joerg Arndt, Apr 07 2013

Examples

			5 is in the list since 2*5 + 1 = 11 divides 2^5 + 1 = 33.
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Second Edition, Cambridge University Press, 2005, p. 85.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Giovanni Resta, Curzon numbers, Numbers Aplenty.

Crossrefs

Cf. A000051, A175865, A224499.

Programs

Mathematica

Select[Range[300], PowerMod[2, #, 2 # + 1] == 2 # &] (* Amiram Eldar, Oct 13 2020 *)

PARI

for(n=0, 10^3, my(m=2*n+1); if( Mod(2,m)^n==Mod(-1,m), print1(n, ", ") ) ); \\ Joerg Arndt, Apr 08 2013