This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085724 #35 Jun 26 2025 01:15:37 %S A085724 4,9,11,23,37,41,49,59,67,83,97,101,103,109,131,137,139,149,167,197, %T A085724 199,227,241,269,271,281,293,347,373,379,421,457,487,523,727,809,881, %U A085724 971,983,997,1061,1063 %N A085724 Numbers k such that 2^k - 1 is a semiprime (A001358). %C A085724 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 %C A085724 1427 and 1487 are also terms. 1277 is the only remaining unknown below them. - _Charles R Greathouse IV_, Jun 05 2013 %C A085724 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 %C A085724 Either a(n) is a prime, or the square of a Mersenne prime exponent. - _M. F. Hasler_, Jun 23 2025 %D A085724 J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 22 2009] %D A085724 J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 25 2009] %H A085724 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a> %H A085724 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a> %H A085724 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a> %e A085724 11 is a member because 2^11 - 1 = 23*89. %t A085724 SemiPrimeQ[n_]:=(n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Range[100],SemiPrimeQ[2^#-1]&] (Noe) %t A085724 Select[Range[1100],PrimeOmega[2^#-1]==2&] (* _Harvey P. Dale_, Feb 18 2018 *) %t A085724 Select[Range[250], Total[Last /@ FactorInteger[2^# - 1, 3]] == 2 &] (* _Eric W. Weisstein_, Jul 28 2022 *) %o A085724 (PARI) issemi(n)=bigomega(n)==2 %o A085724 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 %Y A085724 Cf. A092558, A092559, A092561, A092562. %K A085724 nonn,more %O A085724 1,1 %A A085724 _Jason Earls_, Jul 20 2003 %E A085724 More terms from _Zak Seidov_, Feb 27 2004 %E A085724 More terms from Cunningham project, Mar 23 2004 %E A085724 More terms from the Cunningham project sent by _Robert G. Wilson v_ and _T. D. Noe_, Feb 22 2006 %E A085724 a(41)-a(42) from _Charles R Greathouse IV_, Jun 05 2013