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 A279065 #46 Oct 05 2023 07:00:33
%S A279065 1,2,3,4,5,7,11,19,47,169,907,6829,67931,851891,13034887,237522877,
%T A279065 5057212439,123890683831
%N A279065 Fermi-Dirac primeth recurrence: a(0)=1; thereafter a(n+1) = a(n)-th number of the form p^(2^k) where p is prime and k>=0.
%C A279065 _Daniel Forgues_ (see A182979) and _Reinhard Zumkeller_ (see A213925) describe the increasing sequence of positive integers of the form p^(2^k) where p is prime and k>=0 (A050376 or A084400) as Fermi-Dirac primes, because any positive integer has a unique factorization into distinct terms.
%H A279065 OEIS Wiki, <a href="/wiki/%22Fermi-Dirac_representation%22_of_n">"Fermi-Dirac representation" of n</a>.
%t A279065 nn=10000;FDfactor[n_]:=If[n===1,{},Sort[Join@@Cases[FactorInteger[n],{p_,k_}:>Power[p,Cases[Position[IntegerDigits[k,2]//Reverse,1],{m_}->2^(m-1)]]]]];
%t A279065 FDprimeList=Array[FDfactor,nn,1,Union];
%t A279065 NestWhileList[Part[FDprimeList,#]&,1,#<=Length[FDprimeList]&]
%o A279065 (PARI) lista(kmax) = {my(m = 1, c=0, isp); print1(1, ", "); for(k = 1, kmax, isp = isprimepower(k); if(isp && isp >> valuation(isp, 2) == 1, c++); if(c == m, print1(k,", "); m=k));} \\ _Amiram Eldar_, Oct 05 2023
%Y A279065 Cf. A007097, A050376, A084400, A182979, A213925.
%K A279065 nonn,more
%O A279065 0,2
%A A279065 _Gus Wiseman_, Dec 10 2016
%E A279065 a(15)-a(17) from _Amiram Eldar_, Oct 05 2023