A112797 - OEIS

%I #9 Jan 02 2021 13:22:19

%S 28,244,325,385,730,1025,1729,2188,5185,6562,7777,16385,26245,36865,

%T 46657,49153,55297,82945,93313,221185,354295,419905,531442,559873,

%U 589825,663553,708589,884737,1119745,1572865,1594324,1889569,2985985

%N Pierpont 3-almost primes. 3-almost primes of form (2^K)*(3^L)+1.

%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) = 3.

%e a(1) = 28 = (2^0)*(3^3)+1 = 2 * 2 * 7.

%e a(2) = 244 = (2^0)*(3^5)+1 = 2 * 2 * 61.

%e a(3) = 325 = (2^2)*(3^4)+1 = 5 * 5 * 13.

%e a(4) = 385 = (2^7)*(3^1)+1 = 5 * 7 * 11.

%e a(11) = 7777 = (2^5)*(3^5)+1 = 7 * 11 * 101.

%e a(115) = 94143178828 = (2^0)*(3^23)+1 = 2 * 2 * 23535794707.

%e a(119) = 137438953473 = (2^37)*(3^0)+1 = 3 * 1777 * 25781083.

%e a(196) = 281474976710657 = (2^48)*(3^0)+1 = 193 * 65537 * 22253377.

%t Take[Select[2^#[[1]] 3^#[[2]] + 1 & /@ Tuples[Range[0, 20], 2],

%t PrimeOmega[ #]  ==  3 &] // Union, 40] (* _Harvey P. Dale_, Jan 02 2021 *)

%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)==3, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017

%Y Intersection of A014612 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 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 A113740 gives the Pierpont 8-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 easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 08 2005

%E Extended by _Ray Chandler_, Nov 08 2005