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A309646
Digits of the 10-adic integer (-71/9)^(1/3).
3
1, 6, 3, 1, 6, 7, 2, 5, 4, 5, 8, 8, 0, 7, 7, 0, 9, 9, 6, 5, 4, 1, 8, 9, 2, 8, 3, 5, 3, 4, 6, 9, 6, 8, 4, 3, 0, 2, 6, 7, 5, 7, 5, 7, 9, 3, 7, 7, 9, 7, 6, 3, 2, 1, 5, 3, 4, 8, 4, 2, 4, 9, 0, 5, 5, 9, 0, 4, 4, 8, 0, 9, 7, 5, 2, 2, 3, 3, 5, 9, 8, 9, 3, 7, 0, 3, 1, 6, 0, 2, 0, 3, 9, 7, 6, 5, 3, 1, 3, 1
OFFSET
0,2
LINKS
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 + 71) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
EXAMPLE
1^3 == 1 (mod 10).
61^3 == 81 (mod 10^2).
361^3 == 881 (mod 10^3).
1361^3 == 8881 (mod 10^4).
61361^3 == 88881 (mod 10^5).
761361^3 == 888881 (mod 10^6).
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-71/9+O(2^N))^(1/3), 2^N), Mod((-71/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309646(n)
ary = [1]
a = 1
n.times{|i|
b = (a + 7 * (9 * a ** 3 + 71)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A309646(100)
CROSSREFS
Sequence in context: A365477 A066717 A176395 * A195494 A154969 A192741
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 11 2019
STATUS
approved