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A309700 Digits of the 8-adic integer 7^(1/7). 5
7, 6, 1, 0, 1, 6, 4, 1, 7, 3, 6, 4, 4, 5, 3, 3, 4, 2, 0, 0, 6, 2, 5, 4, 2, 6, 6, 3, 2, 2, 6, 1, 0, 3, 5, 6, 1, 6, 6, 7, 0, 6, 6, 7, 7, 5, 3, 2, 2, 7, 5, 5, 1, 7, 5, 7, 1, 1, 1, 2, 5, 0, 4, 3, 2, 5, 3, 0, 3, 3, 1, 7, 3, 4, 5, 4, 5, 1, 1, 2, 2, 7, 0, 6, 7, 1, 4, 4, 6, 7, 6, 2, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Wikipedia, Hensel's Lemma.
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + b(n-1)^7 - 7 mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n.
PROG
(PARI) N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/7)), 8), N)
(Ruby)
def A309700(n)
ary = [7]
a = 7
n.times{|i|
b = (a + a ** 7 - 7) % (8 ** (i + 2))
ary << (b - a) / (8 ** (i + 1))
a = b
}
ary
end
p A309700(100)
CROSSREFS
Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), this sequence (k=8), A225458 (k=10).
Cf. A225445.
Sequence in context: A256319 A324688 A334400 * A353823 A247444 A319331
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 13 2019
STATUS
approved

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Last modified March 1 06:29 EST 2024. Contains 370430 sequences. (Running on oeis4.)