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 A346153 #9 Oct 15 2023 05:15:06
%S A346153 1,2,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%T A346153 5,5,5,5,5,5,5,5,5,5,5,5,7,5,7,5,5,5,7,5,7,5,7,7,7,7,7,7,7,7,7,7,7,7,
%U A346153 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N A346153 a(n) = A346152(n!).
%C A346153 Erdős and Selfridge (1982) proved that if f(n) = primepi(a(n)) (or, equivalently, a(n) = prime(f(n))), then |f(n+1) - f(n)| <= 1, and that for infinitely many values of n, f(n+1) = f(n) - 1.
%H A346153 Amiram Eldar, <a href="/A346153/b346153.txt">Table of n, a(n) for n = 1..10000</a>
%H A346153 Paul Erdős, <a href="https://users.renyi.hu/~p_erdos/1982-08.pdf">Miscellaneous problems in number theory</a>, Proceedings of the Eleventh Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, Man., 1981), Congr. Numer., Vol. 34 (1982), pp. 25-45.
%H A346153 Paul Erdős and John L. Selfridge, <a href="http://www.jstor.org/stable/2320567">Problem 6339</a>, Advanced problems, The American Mathematical Monthly, Vol. 88, No. 4 (1981), p. 294; <a href="http://www.jstor.org/stable/2975853">Factorizationf n!, solution to problem 6339</a>, solved by the proposers, ibid., Vol. 89, No. 10 (1982), pp. 790-794.
%F A346153 a(n) = A346152(A000142(n)).
%F A346153 Lim_{n->oo} a(n)/sqrt(n) = exp(gamma - 1/2), where gamma is Euler's constant (A001620) (Erdős and Selfridge, 1982).
%t A346153 f[1] = 1; f[n_] := Module[{fct = FactorInteger[n], prods, ind}, prods = Rest @ FoldList[Times, 1, Power @@@ fct]; ind = FirstPosition[prods^2, _?(# > n &)][[1]]; fct[[ind, 1]]]; a[n_] := f[n!]; Array[a, 100]
%Y A346153 Cf. A000142, A001620, A073004, A346152.
%K A346153 nonn
%O A346153 1,2
%A A346153 _Amiram Eldar_, Jul 07 2021