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 A309903 #11 Aug 26 2019 11:23:05
%S A309903 0,1,21,71,196,2071,2071,33321,345821,736446,8548946,18314571,
%T A309903 18314571,994877071,994877071,25408939571,86444095821,239031986446,
%U A309903 1001971439571,16260760502071,92554705814571,283289569095821,1236963885502071,8389521258548946
%N A309903 Approximation of the 5-adic integer exp(-5) up to 5^n.
%C A309903 In p-adic field, the exponential function exp(x) is defined as Sum_{k>=0} x^k/k!. When extended to a function over the metric completion of the p-adic field, exp(x) has radius of convergence p^(-1/(p-1)) (i.e., exp(x) converges for x such that |x|_p < p^(-1/(p-1)), where |x|_p is the p-adic metric). As a result, for odd primes p, exp(p) is well-defined in p-adic field, and exp(4) is well defined in 2-adic field.
%C A309903 a(n) is the multiplicative inverse of A309902(n) modulo 5^n.
%H A309903 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%o A309903 (PARI) a(n) = lift(exp(-5 + O(5^n)))
%Y A309903 Cf. A309902.
%Y A309903 The 5-adic expansion of exp(5) is given by A309975.
%Y A309903 Approximations of exp(-p) in p-adic field: A309901 (p=3), this sequence (p=5), A309905 (p=7).
%K A309903 nonn
%O A309903 0,3
%A A309903 _Jianing Song_, Aug 21 2019