

A085724


Numbers n such that 2^n  1 is a semiprime (A001358).


12



4, 9, 11, 23, 37, 41, 49, 59, 67, 83, 97, 101, 103, 109, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 523, 727, 809, 881, 971, 983, 997, 1061, 1063
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OFFSET

1,1


COMMENTS

Subsequence of A000430. Apart from 4, 9, and 49 composites in this sequence are greater than 1.9e7.  Charles R Greathouse IV, Jun 05 2013
1427 and 1487 are also terms. 1277 is the only remaining unknown below them.  Charles R Greathouse IV, Jun 05 2013
Among the known terms only 11, 23, 83 and 131 are in A002515, that is, they are the only known values for n such that (2^n  1)/(2*n + 1) is prime.  Jianing Song, Jan 22 2019


REFERENCES

J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 5660. ASIN: B002ACVZ6O [From Jason Earls, Nov 22 2009]
J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 5660. ASIN: B002ACVZ6O [From Jason Earls, Nov 25 2009]


LINKS

Table of n, a(n) for n=1..42.
S. S. Wagstaff, Jr., The Cunningham Project


EXAMPLE

11 is a member because 2^11  1 = 23*89.


MATHEMATICA

SemiPrimeQ[n_]:=(n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Range[100], SemiPrimeQ[2^#1]&] (Noe)
Select[Range[1100], PrimeOmega[2^#1]==2&] (* Harvey P. Dale, Feb 18 2018 *)


PROG

(PARI) issemi(n)=bigomega(n)==2
is(n)=if(isprime(n), issemi(2^n1), my(q); isprimepower(n, &q)==2 && ispseudoprime(2^q1) && ispseudoprime((2^n1)/(2^q1))) \\ Charles R Greathouse IV, Jun 05 2013


CROSSREFS

Cf. A092558, A092559, A092561, A092562.
Sequence in context: A179055 A277428 A002641 * A106854 A099458 A069219
Adjacent sequences: A085721 A085722 A085723 * A085725 A085726 A085727


KEYWORD

nonn,more


AUTHOR

Jason Earls, Jul 20 2003


EXTENSIONS

More terms from Zak Seidov, Feb 27 2004
More terms from Cunningham project, Mar 23 2004
More terms from the Cunningham project sent by Robert G. Wilson v and T. D. Noe, Feb 22 2006
a(41)a(42) from Charles R Greathouse IV, Jun 05 2013


STATUS

approved



