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%I M1395
%S 2,5,11,23,47,191,383,6143,786431,51539607551,824633720831,
%T 26388279066623,108086391056891903,55340232221128654847,
%U 226673591177742970257407,59421121885698253195157962751,30423614405477505635920876929023
%N Primes of form 3*2^n -1.
%C a(1) = 2, define f(k) = 2k+1, then a(n+1) = least prime fff...(a(n)). After 383 the next terem is 6143. We have f(383) = 767 (composite), f(767) = 1535 (composite), f(1565)=3071(composite), f(3071) = 6143 (prime), hence the next term is 6143= ffff(383). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 13 2005
%C If n is in the sequence and m=(n+1)/3 then m is a solution of the equation, sigma(x+sigma(x))=3x (*). Is it true that there is no other solution of (*)? - _Farideh Firoozbakht_, Dec 05 2005
%D H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, pp. 381-384.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A007505/b007505.txt">Table of n, a(n) for n = 1..27</a>
%H Wilfrid Keller, <a href="http://www.prothsearch.net/riesel2.html">List of primes k*2^n - 1 for k < 300</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ThabitibnKurrahNumber.html">Thabit ibn Kurrah Number</a>
%H <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>
%t Reap[For[n = 0, n <= 103, n++, If[PrimeQ[p = 3*2^n - 1], Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Dec 12 2012 *)
%t Select[Table[3 2^n - 1, {n, 0, 100}], PrimeQ] (* _Vincenzo Librandi_, Mar 20 2013 *)
%o (MAGMA) [a: n in [0..200] | IsPrime(a) where a is 3*2^n-1]; // _Vincenzo Librandi_, Mar 20 2013
%Y See A002235 for more terms.
%Y Cf. A039687 (primes of the form 3*2^n+1). [_Bruno Berselli_, Mar 20 2013]
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_, _Robert G. Wilson v_
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