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 A085303 #17 Feb 18 2025 08:58:40
%S A085303 1,2,7,10,14,17,20,23,27,30,33,37,40,43,47,50,53,57,60,63,67,70,73,77,
%T A085303 80,84,87,90,94,97,101,104,108,111,114,118,121,125,128,132,135,139,
%U A085303 142,146,149,153,156,160,164,167,171,174,178,181,185,188,192,196,199,203
%N A085303 Positions of 2 in A085301.
%C A085303 Numbers k such that A085301(k) = 2, i.e., between primorial(k-1) and primorial(k) there are two distinct factorial numbers.
%H A085303 Amiram Eldar, <a href="/A085303/b085303.txt">Table of n, a(n) for n = 1..10000</a>
%F A085303 Solutions x to A085301(x) = 2.
%e A085303 10 is a term since between the 9th and the 10th primorials there are two factorials: 12! and 13!.
%e A085303 14 is a term since between the 13th and the 14th primorials there are two factorials: 17! and 18!.
%e A085303 584 is a term since between the 583rd and the 584th primorials there are two factorials: 745! and 746!.
%t A085303 f[n_] := f[n] = Module[{k = 1, r = Times @@ Prime[Range[n]]}, While[r >= 1, k++; r /= k]; k - 1]; q[n_] := f[n] - f[n - 1] == 2; q[1] = q[2] = True; Select[Range[210], q] (* _Amiram Eldar_, Feb 18 2025 *)
%o A085303 (PARI) f(n) = {my(k = 1); while(n >= 1, k++; n /= k); k-1;}
%o A085303 list(lim) = {my(c = 1, f1 = 1, r = 1, k = 0); print1("1, 2, "); forprime(p = 2, lim, k++; r* = p; f2 = f(r); if(f2 == f1 + 2, print1(k, ", ")); f1 = f2);} \\ _Amiram Eldar_, Feb 18 2025
%Y A085303 Cf. A085301, A002110, A000142.
%K A085303 nonn
%O A085303 1,2
%A A085303 _Labos Elemer_, Jun 26 2003