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 A341687 #12 Feb 19 2021 03:38:14
%S A341687 6,6,1,1,6,1,0,2,0,3,5,1,4,1,3,6,2,0,2,4,3,5,6,3,4,3,5,0,0,4,4,0,1,0,
%T A341687 1,6,2,0,0,3,3,5,1,4,6,1,5,1,5,4,5,5,1,5,1,6,5,6,2,2,0,2,0,5,5,0,5,5,
%U A341687 6,5,1,4,2,2,2,1,2,2,0,5,5,5,2,6,2,0,4,0,1,3,5
%N A341687 Expansion of the 7-adic integer Sum_{k>=0} k!.
%C A341687 For every prime p, since valuation(k!,p) goes to infinity as k increases, Sum_{k>=0} k! is a well-defined p-adic constant.
%C A341687 Conjecture: this constant is transcendental, which means that it is not the root of any polynomial with integer coefficients.
%C A341687 Conjecture: this constant is normal, which means for every septenary (base-7) string s with length k, if we denote N(s,n) as the number of occurrences of s in the first n digits, then lim_{n->inf} N(s,n)/n = 1/7^k.
%H A341687 Jianing Song, <a href="/A341687/b341687.txt">Table of n, a(n) for n = 0..1000</a>
%F A341687 a(n) = (A341683(n+1) - A341683(n))/7^n.
%e A341687 Sum_{k>=0} k! = ...33002610104400534365342026314153020161166.
%o A341687 (PARI) a(n) = my(p=7); lift(sum(k=0, (p-1)*((n+1)+logint((p-1)*(n+1), p)), Mod(k!, p^(n+1)))) \ p^n
%Y A341687 Cf. A341683 (successive approximations of Sum_{k>=0} k!).
%Y A341687 Expansion of Sum_{k>=0} k! in p-adic integers: A341684 (p=2), A341685 (p=3), A341686 (p=5), this sequence (p=7).
%K A341687 nonn,base
%O A341687 0,1
%A A341687 _Jianing Song_, Feb 17 2021