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 A309905 Approximation of the 7-adic integer exp(-7) up to 7^n. 4
 0, 1, 43, 190, 1562, 6364, 56785, 645030, 3115659, 14645261, 14645261, 297120510, 8206427482, 22047714683, 118936725090, 118936725090, 23856744274805, 123555535983608, 588816563958022, 5474057357689369, 51069638099181941, 51069638099181941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. a(n) is the multiplicative inverse of A309904(n) modulo 7^n. LINKS Wikipedia, p-adic number PROG (PARI) a(n) = lift(exp(-7 + O(7^n))) CROSSREFS Cf. A309904. The 7-adic expansion of exp(-7) is given by A309988. Approximations of exp(-p) in p-adic field: A309901 (p=3), A309903 (p=5), this sequence (p=7). Sequence in context: A158628 A123597 A138631 * A142115 A141941 A197887 Adjacent sequences:  A309902 A309903 A309904 * A309906 A309907 A309908 KEYWORD nonn AUTHOR Jianing Song, Aug 21 2019 STATUS approved

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Last modified June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)