A309700 Digits of the 8-adic integer 7^(1/7).

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

Offset

0,1

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A309697 A309698 A309699 * A309701 A309702 A309703

Keyword

nonn,base

Author

Seiichi Manyama, Aug 13 2019

Status

approved