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A007505 Primes of form 3*2^n -1.
(Formerly M1395)
8
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

Heiko Harborth, On h-perfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62; http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from57to62.pdf.

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

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

MATHEMATICA

Reap[For[n = 0, n <= 103, n++, If[PrimeQ[p = 3*2^n - 1], Sow[p]]]][[2, 1]] (* Jean-Fran├žois 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

CROSSREFS

See A002235 for more terms.

Cf. A039687 (primes of the form 3*2^n+1). [Bruno Berselli, Mar 20 2013]

Cf. A010051, subsequence of A083329.

Sequence in context: A105120 A084403 A055011 * A246492 A059411 A126017

Adjacent sequences:  A007502 A007503 A007504 * A007506 A007507 A007508

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified August 28 05:09 EDT 2015. Contains 261118 sequences.