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A007505
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Primes of form 3*2^n -1.
(Formerly M1395)
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7
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2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407, 59421121885698253195157962751, 30423614405477505635920876929023
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OFFSET
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1,1
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COMMENTS
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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
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
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REFERENCES
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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).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..27
Wilfrid Keller, List of primes k*2^n - 1 for k < 300
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
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) [a: n in [0..200] | IsPrime(a) where a is 3*2^n-1]; // Vincenzo Librandi, Mar 20 2013
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CROSSREFS
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See A002235 for more terms.
Cf. A039687 (primes of the form 3*2^n+1). [Bruno Berselli, Mar 20 2013]
Sequence in context: A105120 A084403 A055011 * A059411 A126017 A034468
Adjacent sequences: A007502 A007503 A007504 * A007506 A007507 A007508
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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STATUS
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approved
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