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A309445
Coefficients in 7-adic expansion of 2^(1/5).
11
4, 6, 1, 3, 6, 4, 3, 5, 4, 6, 5, 4, 0, 0, 6, 4, 3, 4, 5, 6, 2, 2, 2, 0, 6, 5, 5, 0, 3, 1, 1, 4, 0, 4, 6, 2, 0, 6, 0, 3, 6, 3, 2, 5, 4, 6, 4, 0, 5, 5, 2, 1, 4, 3, 4, 1, 0, 1, 1, 6, 0, 4, 1, 6, 0, 4, 5, 1, 1, 6, 2, 5, 2, 3, 0, 6, 1, 3, 6, 4, 0, 6, 2, 6, 4, 2, 0, 1, 6, 3, 6, 5, 1, 2, 4, 3, 3, 0, 4, 6, 2
OFFSET
0,1
LINKS
MAPLE
op([1, 3], padic:-rootp(x^5-2, 7, 101)); # Robert Israel, Aug 04 2019
PROG
(Ruby)
require 'OpenSSL'
def f_a(ary, a)
(0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}
end
def df(ary)
(1..ary.size - 1).map{|i| i * ary[i]}
end
def A(c_ary, k, m, n)
x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m
f_ary = c_ary.map{|i| x * i}
f_ary[1] += 1
d_ary = []
ary = [0]
a, mod = k, m
(n + 1).times{|i|
b = a % mod
d_ary << (b - ary[-1]) / m ** i
ary << b
a = f_a(f_ary, b)
mod *= m
}
d_ary
end
def A309445(n)
A([-2, 0, 0, 0, 0, 1], 4, 7, n)
end
p A309445(100)
(PARI) Vecrev(digits(truncate((2+O(7^100))^(1/5)), 7))
CROSSREFS
Cf. A309450.
Digits of p-adic integers:
A290566 (5-adic, 2^(1/3));
A309446 (7-adic, 3^(1/5));
A309447 (7-adic, 4^(1/5));
A309448 (7-adic, 5^(1/5));
A309449 (7-adic, 6^(1/5)).
Sequence in context: A255695 A246489 A343624 * A051261 A247621 A245275
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 03 2019
STATUS
approved

  NODES
COMMUNITY 1
INTERN 1