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 A007505 Primes of form 3*2^n - 1. (Formerly M1395) 15
 2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407, 59421121885698253195157962751, 30423614405477505635920876929023 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 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 REFERENCES H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, pp. 381-384. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..27 Heiko Harborth, On h-perfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62. Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33. Wilfrid Keller, List of primes k*2^n - 1 for k < 300 Amelia Carolina Sparavigna, A recursive formula for Thabit numbers, Politecnico di Torino (Italy, 2019). Amelia Carolina Sparavigna, Composition Operations of Generalized Entropies Applied to the Study of Numbers, International Journal of Sciences (2019) Vol. 8, No. 4, 87-92. Eric Weisstein's World of Mathematics, Thabit ibn Kurrah Number Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime FORMULA a(n) = 3*2^A002235(n)-1. - Zak Seidov, Jul 21 2016 MATHEMATICA Reap[For[n = 0, n <= 103, n++, If[PrimeQ[p = 3*2^n - 1], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 12 2012 *) Select[Table[3 2^n - 1, {n, 0, 100}], PrimeQ] (* Vincenzo Librandi, Mar 20 2013 *) PROG (Magma) [a: n in [0..200] | IsPrime(a) where a is 3*2^n-1]; // Vincenzo Librandi, Mar 20 2013 (Haskell) a007505 n = a007505_list !! (n-1) a007505_list = filter ((== 1) . a010051') a083329_list -- Reinhard Zumkeller, Sep 10 2013 (PARI) for(n=0, 100, if(isprime(t=3<

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Last modified April 24 19:06 EDT 2024. Contains 371962 sequences. (Running on oeis4.)