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A224486
Numbers k such that 2*k+1 divides 2^k+1.
5
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
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
KEYWORD
nonn
AUTHOR
Jayanta Basu, Apr 07 2013
STATUS
approved