

A309901


Approximation of the 3adic 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
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OFFSET

0,3


COMMENTS

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.
a(n) is the multiplicative inverse of A309900(n) modulo 3^n.


LINKS



PROG

(PARI) a(n) = lift(exp(3 + O(3^n)))


CROSSREFS

The 3adic expansion of exp(3) is given by A309866.
Approximations of exp(p) in padic field: this sequence (p=3), A309903 (p=5), A309905 (p=7).


KEYWORD

nonn


AUTHOR



STATUS

approved



