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A309612
Digits of the 10-adic integer (-23/9)^(1/3).
3
7, 3, 7, 0, 2, 3, 9, 5, 2, 5, 7, 6, 5, 0, 9, 7, 8, 3, 4, 4, 5, 4, 0, 2, 6, 6, 7, 3, 5, 0, 3, 9, 9, 3, 5, 0, 4, 6, 7, 6, 8, 0, 3, 6, 6, 9, 4, 3, 8, 8, 5, 2, 7, 6, 8, 3, 7, 4, 2, 0, 0, 2, 6, 4, 8, 9, 1, 5, 7, 9, 7, 3, 6, 8, 3, 1, 7, 3, 5, 1, 5, 6, 5, 4, 0, 4, 6, 1, 0, 1, 3, 4, 2, 0, 8, 2, 7, 2, 3, 8
OFFSET
0,1
LINKS
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n
EXAMPLE
7^3 == 3 (mod 10).
37^3 == 53 (mod 10^2).
737^3 == 553 (mod 10^3).
737^3 == 5553 (mod 10^4).
20737^3 == 55553 (mod 10^5).
320737^3 == 555553 (mod 10^6).
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-23/9+O(2^N))^(1/3), 2^N), Mod((-23/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309612(n)
ary = [7]
a = 7
n.times{|i|
b = (a + 3 * (9 * a ** 3 + 23)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A309612(100)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 10 2019
STATUS
approved