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 A113434 #22 Feb 16 2025 08:32:59
%S A113434 4,9,10,25,49,65,289
%N A113434 Semi-Pierpont semiprimes which are also Pierpont semiprimes.
%C A113434 Semiprimes both of whose prime factors are Pierpont primes (A005109), which are primes of the form (2^K)*(3^L)+1 and where the semiprime is itself of the form (2^K)*(3^L)+1.
%C A113434 No more under 10^50; what is the next element of this sequence?
%C A113434 No more terms <= 10^100. - _Robert Israel_, Mar 10 2017
%C A113434 This sequence is complete, see Links. - _Charlie Neder_, Feb 04 2019
%H A113434 Chris Caldwell, <a href="http://groups.yahoo.com/group/primeform/message/6588/">"Pierpont primes." primeform posting, Oct 25, 2005.</a>
%H A113434 Chris Caldwell, <a href="/A113434/a113434.pdf">"Pierpont primes." primeform posting, Oct 25, 2005.</a> [Cached copy]
%H A113434 Charlie Neder, <a href="/A113434/a113434.txt">Proof of the completeness of this sequence</a>
%H A113434 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>
%H A113434 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F A113434 {a(n)} = intersection of A113432 and A113433. {a(n)} = Semiprimes A001358 of the form (2^K)*(3^L)+1 both of whose factors are of the form (2^K)*(3^L)+1. {a(n)} = {integers P such that, for nonnegative integers I, J, K, L, m, n there is a solution to (2^I)*(3^J)+1 = [(2^K)*(3^L)+1]*[(2^m)*(3^n)+1] where both [(2^K)*(3^L)+1] and [(2^m)*(3^n)+1] are prime}.
%e A113434 a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^0)*(3^0)+1] = (2^0)*(3^1)+1.
%e A113434 a(2) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = (2^3)*(3^0)+1.
%e A113434 a(3) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = (2^0)*(3^2)+1.
%e A113434 a(4) = 25 = 5^2 = [(2^2)*(3^0)+1]*[(2^2)*(3^0)+1] = (2^3)*(3^1)+1.
%e A113434 a(5) = 49 = 7^2 = [(2^1)*(3^1)+1]*[(2^1)*(3^1)+1] = (2^4)*(3^1)+1.
%e A113434 a(6) = 65 = 5*13 = [(2^2)*(3^0)+1]*[(2^2)*(3^1)+1] = (2^6)*(3^0)+1.
%e A113434 a(7) = 289 = 17^2 = [(2^4)*(3^0)+1]*[(2^4)*(3^0)+1] = (2^5)*(3^2)+1.
%p A113434 N:= 10^100: # to get all terms <= N
%p A113434 PP:= select(isprime, {seq(seq(1+2^i*3^j, i=0..ilog2((N-1)/3^j)),j=0..floor(log[3](N-1)))}):
%p A113434 SP:= select(t -> t <= N and t = 1+2^padic:-ordp(t-1,2)*3^padic:-ordp(t-1,3), [seq(seq(PP[i]*PP[j], j=1..i),i=1..nops(PP))]):
%p A113434 sort(convert(SP,list)); # _Robert Israel_, Mar 10 2017
%Y A113434 Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113433.
%K A113434 nonn,fini,full
%O A113434 1,1
%A A113434 _Jonathan Vos Post_, Nov 01 2005