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

1,2

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

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000051, A175865, A224499.

Sequence in context: A366741 A271371 A193978 * A163782 A362140 A226793

Adjacent sequences: A224483 A224484 A224485 * A224487 A224488 A224489

Keyword

nonn

Author

Jayanta Basu, Apr 07 2013

Status

approved