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%I #8 Aug 26 2019 11:23:58
%S 0,1,6,81,456,2956,6081,37331,349831,1521706,3474831,3474831,
%T 101131081,833552956,4495662331,16702693581,16702693581,169290584206,
%U 1695169490456,16953958552956,55100931209206,436570657771706,2343919290584206,9496476663631081
%N Approximation of the 5-adic integer exp(5) up to 5^n.
%C 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 a(n) is the multiplicative inverse of A309903(n) modulo 5^n.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%o (PARI) a(n) = lift(exp(5 + O(5^n)))
%Y Cf. A309903.
%Y The 5-adic expansion of exp(5) is given by A309888.
%Y Approximations of exp(p) in p-adic field: A309900 (p=3), this sequence (p=5), A309904 (p=7).
%K nonn
%O 0,3
%A _Jianing Song_, Aug 21 2019
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