%I M1395 #60 Jul 18 2024 00:03:23

%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_, 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 Heiko Harborth, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from57to62.pdf">On h-perfect numbers</a>, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62.

%H Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k*2^n - 1 for k < 300</a>

%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.2638790">A recursive formula for Thabit numbers</a>, Politecnico di Torino (Italy, 2019).

%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2044">Composition Operations of Generalized Entropies Applied to the Study of Numbers</a>, International Journal of Sciences (2019) Vol. 8, No. 4, 87-92.

%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>

%F a(n) = 3*2^A002235(n)-1. - _Zak Seidov_, Jul 21 2016

%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

%o (Haskell)

%o a007505 n = a007505_list !! (n-1)

%o a007505_list = filter ((== 1) . a010051') a083329_list

%o -- _Reinhard Zumkeller_, Sep 10 2013

%o (PARI) for(n=0,100, if(isprime(t=3<<n-1), print1(t", "))) \\ _Charles R Greathouse IV_, Feb 07 2017

%Y Subsequence of A083329.

%Y See A002235 for more terms.

%Y Cf. A039687 (primes of the form 3*2^n+1).

%Y Cf. A010051.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_, _Robert G. Wilson v_