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 A338460 #79 Feb 07 2025 16:00:17
%S A338460 3,6,1,4,7,9,3,7,0,3,1,9,2,5,2,5,4,4,7,3,8,6,5,3,6,6,2,5,6,0,3,4,5,4,
%T A338460 6,3,3,5,3,1,5,1,6,5,9,6,9,4,7,5,0,2,2,6,6,1,1,1,5,9,9,9,7,7,4,6,2,5,
%U A338460 1,8,2,9,8,6,1,3,6,1,8,5,7,5,4,3,2,8,1,8,6,2,8,2,1,5,7,1,1,5,9,6,3,3,0,8,1
%N A338460 Decimal expansion of the largest real root of e^(x-1) = Gamma(x+1).
%C A338460 Decimal expansion of the constant value for which the average and the minimum prime gaps are equal for the prime number sequences of higher order P', P'', P''', and P'''' as represented by A333242, A262275, A333243 and A333244.
%C A338460 x-1 is the smallest average gap size for the set of all prime numbers P. - _Michael P. May_, Jan 26 2025
%F A338460 x| (log(x!))^n * (log(x!) + 1) = x * (x-1)^n, for n >= 0
%e A338460 3.61479370319252544738653662560345463353151659694750...
%p A338460 Digits:= 155:
%p A338460 fsolve(exp(x-1)=GAMMA(x+1), x=3..4); # _Alois P. Heinz_, Feb 01 2021
%t A338460 RealDigits[x /. FindRoot[LogGamma[x + 1] - x + 1, {x, 3}, WorkingPrecision -> 110], 10, 105][[1]] (* _Amiram Eldar_, Feb 01 2021 *)
%o A338460 (PARI) solve(x=3,4,lngamma(x+1)-x+1) \\ _Hugo Pfoertner_, Feb 01 2021
%Y A338460 Cf. A333242, A262275, A333243, A333244.
%Y A338460 Cf. A001113, A078335, A336763.
%K A338460 nonn,cons
%O A338460 1,1
%A A338460 _Michael P. May_, Jan 31 2021