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A224486 Numbers k such that 2*k+1 divides 2^k+1. 4

%I

%S 1,2,5,6,9,14,18,21,26,29,30,33,41,50,53,54,65,69,74,78,81,86,89,90,

%T 98,105,113,114,125,134,138,141,146,153,158,165,173,174,186,189,194,

%U 198,209,210,221,230,233,245,249,254,261,270,273,278,281,285,293

%N Numbers k such that 2*k+1 divides 2^k+1.

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

%C Sequence 2*a(n)+1 apparently is A175865 (certainly it is not A003629). - _Joerg Arndt_, Apr 07 2013

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

%H Amiram Eldar, <a href="/A224486/b224486.txt">Table of n, a(n) for n = 1..10000</a>

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Curzon_number/">Curzon numbers</a>, Numbers Aplenty.

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

%t Select[Range[300], PowerMod[2, #, 2 # + 1] == 2 # &] (* _Amiram Eldar_, Oct 13 2020 *)

%o (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

%Y Cf. A000051, A175865, A224499.

%K nonn

%O 1,2

%A _Jayanta Basu_, Apr 07 2013

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Last modified March 1 02:07 EST 2021. Contains 341732 sequences. (Running on oeis4.)