

A224486


Numbers n such that 2n+1 divides 2^n+1.


3



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
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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, p. 85.


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

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


MATHEMATICA

Select[Range[300], IntegerQ[(2^# + 1)/(2*# + 1)] &]


PROG

(PARI) for(n=1, 10^3, if((2^n+1)%(2*n+1)==0, print1(n, ", "))); \\ Joerg Arndt, Apr 07 2013
/* the following program is significantly faster; positive terms only: */
(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

Sequence in context: A255737 A271371 A193978 * A163782 A226793 A255747
Adjacent sequences: A224483 A224484 A224485 * A224487 A224488 A224489


KEYWORD

nonn


AUTHOR

Jayanta Basu, Apr 07 2013


STATUS

approved



