%I #8 Feb 06 2017 09:59:39
%S 1999004627104432129,4052555153018976268,8754997675608244225,
%T 9606056659007943745,11832592569282330625,22769912080611422209,
%U 68309736241834266625,354577405862133891073,12449449430074295092225
%N Pierpont 8-almost primes. 8-almost primes of form (2^K)*(3^L)+1.
%H Charles R Greathouse IV, <a href="/A113740/b113740.txt">Table of n, a(n) for n = 1..993</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>
%F a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 8.
%e a(1) = 1999004627104432129 = (2^18)*(3^27)+1 = 7 * 13 * 19 * 109 * 127 * 181 * 6949 * 66403.
%e a(2) = 4052555153018976268 = (2^0)*(3^39)+1 = 2 * 2 * 7 * 79 * 157 * 2887 * 10141 * 398581.
%e a(3) = 8754997675608244225 = (2^55)*(3^5)+1 = 5 * 5 * 11 * 11 * 1201 * 1229 * 16451 * 119191.
%e a(4) = 9606056659007943745 = (2^6)*(3^36)+1 = 5 * 13 * 17 * 89 * 109 * 281 * 18793 * 169693.
%e a(13) = 717897987691852588770250 = (2^0)*(3^50)+1 = 2 * 5 * 5 * 5 * 101 * 1181 * 394201 * 61070817601.
%e a(29) = 1570042899082081611640534564 = (2^0)*(3^57)+1 = 2 * 2 * 7 * 2851 * 3079 * 53923 * 101917 * 1162320517.
%o (PARI) list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==8, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 06 2017
%Y Intersection of A046310 and A055600.
%Y A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
%Y A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
%Y A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
%Y A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
%Y A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
%Y A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 08 2005
%E Extended by _Ray Chandler_, Nov 08 2005