Search: id:A111344
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%I A111344
%S A111344 513,13825,32769,59050,110593,157465,177148,186625,262145,279937,497665,
%T A111344 1259713,1327105,2097153,2125765,2519425,4718593,4782970,5668705,
%U A111344 6718465,17915905,18874369,22674817,33554433,38263753,56623105
%N A111344 Pierpont 4-almost primes. 4-almost primes of form (2^K)*(3^L)+1.
%H A111344 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PierpontPrime.html">Pierpont Prime</a>
%H A111344 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlmostPrime.html">Almost Prime</a>
%F A111344 a(n) is in this sequence iff there exist nonnegative integers K and L 
               such that Omega((2^K)*(3^L)+1) = 4.
%e A111344 a(1) = 513 = (2^9)*(3^0)+1 = 3 * 3 * 3 * 19.
%e A111344 a(2) = 13825 = (2^9)*(3^3)+1 = 5 * 5 * 7 * 79.
%e A111344 a(3) = 32769 = (2^15)*(3^0)+1 = 3 * 3 * 11 * 331.
%e A111344 a(4) = 59050 = (2^0)*(3^10)+1 = 2 * 5 * 5 * 1181.
%e A111344 a(10) = 279937 = (2^7)*(3^7)+1 = 7 * 7 * 29 * 197 (lots of sevens).
%e A111344 a(24) = 33554433 = (2^25)*(3^0) = 3 * 11 * 251 * 4051.
%e A111344 a(60) = 31381059610 = (2^0)*(3^22)+1 = 2 * 5 * 5501 * 570461.
%e A111344 a(168) = 16677181699666570 = (2^0)*(3^34)+1 = 2 * 5 * 956353 * 1743831169.
%Y A111344 Intersection of A014613 and A055600.
%Y A111344 A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
%Y A111344 A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
%Y A111344 A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.
%Y A111344 Sequence in context: A060947 A066697 A076338 this_sequence A017681 A013957 
               A036087
%Y A111344 Adjacent sequences: A111341 A111342 A111343 this_sequence A111345 A111346 
               A111347
%K A111344 easy,nonn
%O A111344 1,1
%A A111344 Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 08 2005
%E A111344 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 08 2005

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