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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 21:04 EST 2018. Contains 317331 sequences. (Running on oeis4.)