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 A111345 #8 Feb 16 2025 08:32:58 %S A111345 4375,19684,7077889,7962625,34012225,100663297,129140164,452984833, %T A111345 459165025,544195585,644972545,918330049,5159780353,7346640385, %U A111345 8589934593,13947137605,14495514625,23219011585,27518828545,28991029249 %N A111345 Pierpont 5-almost primes. 5-almost primes of form (2^K)*(3^L)+1. %H A111345 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a> %H A111345 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a> %F A111345 a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 5. %e A111345 a(1) = 4375 = (2^1)*(3^7)+1 = 5 * 5 * 5 * 5 * 7. %e A111345 a(2) = 19684 = (2^0)*(3^9)+1 = 2 * 2 * 7 * 19 * 37. %e A111345 a(3) = 7077889 = (2^18)*(3^3)+1 = 7 * 13 * 13 * 31 * 193 (prime factors each have all odd digits). %e A111345 a(4) = 7962625 = (2^15)*(3^5)+1 = 5 * 5 * 5 * 11 * 5791 (again, coincidentally, prime factors each have all odd %e A111345 digits). %e A111345 a(7) = 129140164 = (2^0)*(3^17)+1 = 2 * 2 * 103 * 307 * 1021. %e A111345 a(15) = 8589934593 = (2^33)*(3^0)+1 = 3 * 3 * 67 * 683 * 20857. %e A111345 a(21) = 34359738369 = (2^35)*(3^0)+1 = 3 * 11 * 43 * 281 * 86171. %e A111345 a(30) = 793437161473 = (2^11)*(3^18)+1 = 11 * 11 * 11 * 43 * 13863281. %e A111345 a(32) = 847288609444 = (2^0)*(3^25)+1 = 2 * 2 * 61 * 151 * 22996651. %e A111345 a(47) = 68630377364884 = (2^0)*(3^29)+1 = 2 * 2 * 523 * 6091 * 5385997. %e A111345 a(48) = 70368744177665 = (2^46)*(3^0)+1 = 5 * 277 * 1013 * 1657 * 30269. %e A111345 a(81) = 50031545098999708 = (2^0)*(3^35)+1 = 2 * 2 * 61 * 547 * 374857981681. %e A111345 a(89) = 144115188075855873 = (2^57)*(3^0)+1 = 3 * 3 * 571 * 174763 * 160465489. %e A111345 a(99) = 450283905890997364 = (2^0)*(3^37)+1 = 2 * 2 * 18427 * 107671 * 56737873. %e A111345 a(113) = 4611686018427387905 = (2^62)*(3^0)+1 = 5 * 5581 * 8681 * 49477 * 384773. %o A111345 (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)==5, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017 %Y A111345 Intersection of A014614 and A055600. %Y A111345 A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1. %Y A111345 A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1. %Y A111345 A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1. %Y A111345 A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1. %Y A111345 A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1. %Y A111345 A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1. %Y A111345 A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1. %Y A111345 A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1. %K A111345 easy,nonn %O A111345 1,1 %A A111345 _Jonathan Vos Post_, Nov 08 2005 %E A111345 Extended by _Ray Chandler_, Nov 08 2005