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A309600
Digits of the 10-adic integer (17/9)^(1/3).
36
7, 1, 6, 8, 7, 0, 3, 3, 3, 6, 5, 2, 7, 8, 7, 2, 6, 7, 1, 1, 0, 3, 3, 2, 4, 5, 6, 5, 3, 6, 5, 3, 3, 3, 7, 5, 2, 4, 7, 5, 0, 2, 9, 0, 6, 7, 0, 8, 8, 6, 6, 7, 0, 1, 2, 4, 5, 3, 2, 8, 6, 9, 7, 3, 1, 6, 6, 9, 5, 0, 1, 6, 4, 6, 8, 0, 3, 8, 5, 9, 6, 1, 3, 5, 3, 7, 9, 7, 2, 3, 6, 6, 9, 0, 0, 0, 5, 3, 7, 7, 2
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 - 17) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
EXAMPLE
7^3 == 3 (mod 10).
17^3 == 13 (mod 10^2).
617^3 == 113 (mod 10^3).
8617^3 == 1113 (mod 10^4).
78617^3 == 11113 (mod 10^5).
78617^3 == 111113 (mod 10^6).
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((17/9+O(2^N))^(1/3), 2^N), Mod((17/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309600(n)
ary = [7]
a = 7
n.times{|i|
b = (a + 3 * (9 * a ** 3 - 17)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A309600(100)
CROSSREFS
10-adic integer x.
A225404 (x^3 = ...000003).
A225405 (x^3 = ...000007).
A225406 (x^3 = ...000009).
A153042 (x^3 = ...111111).
this sequence (x^3 = ...111113).
A309601 (x^3 = ...111117).
A309602 (x^3 = ...111119).
A309603 (x^3 = ...222221).
A225410 (x^3 = ...222223).
A309604 (x^3 = ...222227).
A309605 (x^3 = ...222229).
A309606 (x^3 = ...333331).
A225402 (x^3 = ...333333).
A309569 (x^3 = ...333337).
A309570 (x^3 = ...333339).
A309595 (x^3 = ...444441).
A309608 (x^3 = ...444443).
A309609 (x^3 = ...444447).
A309610 (x^3 = ...444449).
A309611 (x^3 = ...555551).
A309612 (x^3 = ...555553).
A309613 (x^3 = ...555557).
A309614 (x^3 = ...555559).
A309640 (x^3 = ...666661).
A309641 (x^3 = ...666663).
A225411 (x^3 = ...666667).
A309642 (x^3 = ...666669).
A309643 (x^3 = ...777771).
A309644 (x^3 = ...777773).
A225401 (x^3 = ...777777).
A309645 (x^3 = ...777779).
A309646 (x^3 = ...888881).
A309647 (x^3 = ...888883).
A309648 (x^3 = ...888887).
A225412 (x^3 = ...888889).
A225409 (x^3 = ...999991).
A225408 (x^3 = ...999993).
A225407 (x^3 = ...999997).
Sequence in context: A060625 A145423 A019796 * A190264 A322663 A231927
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 09 2019
STATUS
approved