%I
%S 0,1,43,190,1562,6364,56785,645030,3115659,14645261,14645261,
%T 297120510,8206427482,22047714683,118936725090,118936725090,
%U 23856744274805,123555535983608,588816563958022,5474057357689369,51069638099181941,51069638099181941
%N Approximation of the 7adic integer exp(7) up to 7^n.
%C In padic 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 padic field, exp(x) has radius of convergence p^(1/(p1)) (i.e., exp(x) converges for x such that x_p < p^(1/(p1)), where x_p is the padic metric). As a result, for odd primes p, exp(p) is welldefined in padic field, and exp(4) is well defined in 2adic field.
%C a(n) is the multiplicative inverse of A309904(n) modulo 7^n.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Padic_number">padic number</a>
%o (PARI) a(n) = lift(exp(7 + O(7^n)))
%Y Cf. A309904.
%Y The 7adic expansion of exp(7) is given by A309988.
%Y Approximations of exp(p) in padic field: A309901 (p=3), A309903 (p=5), this sequence (p=7).
%K nonn
%O 0,3
%A _Jianing Song_, Aug 21 2019
