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 A113739 #8 Feb 16 2025 08:32:59 %S A113739 339738625,10460353204,83682825625,669462604993,2641807540225, %T A113739 3761479876609,7625597484988,18075490334785,35184372088833, %U A113739 481469424205825,488038239039169,570630428688385,1125899906842625 %N A113739 Pierpont 7-almost primes. 7-almost primes of form (2^K)*(3^L)+1. %H A113739 Charles R Greathouse IV, <a href="/A113739/b113739.txt">Table of n, a(n) for n = 1..716</a> %H A113739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a> %H A113739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a> %F A113739 a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 7. %e A113739 a(1) = 339738625 = (2^22)*(3^4)+1 = 5 * 5 * 5 * 17 * 29 * 37 * 149. %e A113739 a(2) = 10460353204 = (2^0)*(3^21)+1 = 2 * 2 * 7 * 7 * 43 * 547 * 2269. %e A113739 a(3) = 83682825625 = (2^3)*(3^21)+1 = 5 * 5 * 5 * 5 * 7 * 631 * 30313. %e A113739 a(4) = 669462604993 = (2^6)*(3^21)+1 = 7 * 13 * 19 * 31 * 67 * 277 * 673. %e A113739 a(7) = 7625597484988 = (2^0)*(3^27)+1 = 2 * 2 * 7 * 19 * 37 * 19441 * 19927. %e A113739 a(9) = 35184372088833 = (2^45)*(3^0)+1 = 3 * 3 * 3 * 11 * 19 * 331 * 18837001. %e A113739 a(13) = 1125899906842625 = (2^50)*(3^0)+1 = 5 * 5 * 5 * 41 * 101 * 8101 * 268501. %e A113739 a(16) = 5559060566555524 = (2^0)*(3^33)+1 = 2 * 2 * 7 * 67 * 661 * 25411 * 176419. %e A113739 a(28) = 9223372036854775809 = (2^63)*(3^0)+1 = 3 * 3 * 3 * 19 * 43 * 5419 * 77158673929. %o A113739 (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)==7, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017 %Y A113739 Intersection of A046308 and A055600. %Y A113739 A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1. %Y A113739 A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1. %Y A113739 A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1. %Y A113739 A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1. %Y A113739 A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1. %Y A113739 A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1. %Y A113739 A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1. %Y A113739 A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1. %K A113739 nonn %O A113739 1,1 %A A113739 _Jonathan Vos Post_, Nov 08 2005 %E A113739 Extended by _Ray Chandler_, Nov 08 2005