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 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 22 2009]
J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 25 2009]
LINKS
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Mersenne Number
Eric Weisstein's World of Mathematics, Semiprime
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 *)
Select[Range[250], Total[Last /@ FactorInteger[2^# - 1, 3]] == 2 &] (* Eric W. Weisstein, Jul 28 2022 *)
PROG
(PARI) issemi(n)=bigomega(n)==2
is(n)=if(isprime(n), issemi(2^n-1), my(q); isprimepower(n, &q)==2 && ispseudoprime(2^q-1) && ispseudoprime((2^n-1)/(2^q-1))) \\ Charles R Greathouse IV, Jun 05 2013
CROSSREFS
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