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A309699 Digits of the 6-adic integer 5^(1/5). 6
5, 4, 0, 3, 1, 5, 0, 0, 3, 3, 2, 1, 3, 0, 0, 3, 4, 3, 1, 1, 1, 1, 1, 4, 3, 4, 0, 5, 3, 1, 1, 5, 3, 3, 0, 2, 2, 2, 5, 3, 5, 5, 2, 5, 2, 2, 2, 3, 4, 2, 0, 5, 4, 3, 3, 2, 0, 0, 4, 1, 1, 5, 5, 5, 0, 0, 1, 4, 3, 5, 4, 5, 1, 5, 5, 0, 5, 4, 0, 4, 4, 4, 4, 3, 4, 4, 0, 4, 3, 4, 0, 5, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
x = ...513045,
x^2 = ...433521,
x^3 = ...051525,
x^4 = ...354241,
x^5 = ...000005.
LINKS
Wikipedia, Hensel's Lemma.
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + b(n-1)^5 - 5 mod 6^n for n > 1, then a(n) = (b(n+1) - b(n))/6^n.
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((5+O(2^N))^(1/5), 2^N), Mod((5+O(3^N))^(1/5), 3^N))), 6), N)
(Ruby)
def A309699(n)
ary = [5]
a = 5
n.times{|i|
b = (a + a ** 5 - 5) % (6 ** (i + 2))
ary << (b - a) / (6 ** (i + 1))
a = b
}
ary
end
p A309699(100)
CROSSREFS
Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), this sequence (k=6), A309700 (k=8), A225458 (k=10).
Cf. A309448.
Sequence in context: A185579 A197134 A049470 * A153106 A021189 A320411
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 13 2019
STATUS
approved

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Last modified March 4 16:59 EST 2024. Contains 370532 sequences. (Running on oeis4.)