

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
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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 hperfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 5762; 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. 381384.
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^n1 (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]] (* JeanFrançois 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^n1]; // Vincenzo Librandi, Mar 20 2013
(Haskell)
a007505 n = a007505_list !! (n1)
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



