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 A309900 Approximation of the 3-adic integer exp(3) up to 3^n. 3
 0, 1, 4, 13, 67, 229, 229, 958, 958, 7519, 27202, 27202, 204349, 1267231, 1267231, 10833169, 39530983, 125624425, 125624425, 125624425, 1287885892, 4774670293, 15235023496, 46616083105, 140759261932, 140759261932, 988047871375, 3529913699704, 11155511184691 (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 A309901(n) modulo 3^n. LINKS Wikipedia, p-adic number PROG (PARI) a(n) = lift(exp(3 + O(3^n))) CROSSREFS Cf. A309901. The 3-adic expansion of exp(3) is given by A317675. Approximations of exp(p) in p-adic field: this sequence (p=3), A309902 (p=5), A309904 (p=7). Sequence in context: A129433 A157311 A318600 * A096805 A009221 A009239 Adjacent sequences:  A309897 A309898 A309899 * A309901 A309902 A309903 KEYWORD nonn AUTHOR Jianing Song, Aug 21 2019 STATUS approved

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Last modified June 13 12:26 EDT 2021. Contains 344996 sequences. (Running on oeis4.)