The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309901 Approximation of the 3-adic integer exp(-3) up to 3^n. 3
 0, 1, 7, 25, 52, 52, 538, 1267, 1267, 1267, 20950, 20950, 198097, 1260979, 1260979, 6043948, 6043948, 92137390, 92137390, 866978368, 2029239835, 5516024236, 26436730642, 57817790251, 246104147905, 810963220867, 1658251830310, 6741983486968, 21993178456942 (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 A309900(n) modulo 3^n. LINKS Wikipedia, p-adic number PROG (PARI) a(n) = lift(exp(-3 + O(3^n))) CROSSREFS Cf. A309900. The 3-adic expansion of exp(-3) is given by A309866. Approximations of exp(-p) in p-adic field: this sequence (p=3), A309903 (p=5), A309905 (p=7). Sequence in context: A269589 A278874 A137380 * A094672 A179436 A254963 Adjacent sequences:  A309898 A309899 A309900 * A309902 A309903 A309904 KEYWORD nonn AUTHOR Jianing Song, Aug 21 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 18 08:52 EDT 2021. Contains 345098 sequences. (Running on oeis4.)