Search: a309603 -id:a309603
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A309600
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Digits of the 10-adic integer (17/9)^(1/3).
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+10
36
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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
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OFFSET
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0,1
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LINKS
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FORMULA
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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.
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EXAMPLE
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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).
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PROG
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(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)
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
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CROSSREFS
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10-adic integer x.
this sequence (x^3 = ...111113).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A309645
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Digits of the 10-adic integer (11/9)^(1/3).
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+10
3
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9, 5, 8, 6, 6, 5, 0, 7, 6, 0, 5, 1, 0, 8, 9, 4, 8, 5, 8, 5, 6, 2, 2, 5, 2, 1, 8, 7, 6, 9, 9, 8, 2, 3, 8, 1, 0, 5, 8, 5, 7, 0, 0, 9, 6, 7, 4, 2, 0, 6, 6, 7, 7, 1, 2, 4, 1, 7, 9, 1, 2, 5, 4, 8, 7, 7, 3, 4, 4, 9, 1, 7, 6, 9, 6, 7, 0, 7, 4, 1, 3, 3, 6, 9, 7, 4, 6, 9, 8, 8, 5, 9, 0, 0, 1, 5, 4, 0, 5, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
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EXAMPLE
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9^3 == 9 (mod 10).
59^3 == 79 (mod 10^2).
859^3 == 779 (mod 10^3).
6859^3 == 7779 (mod 10^4).
66859^3 == 77779 (mod 10^5).
566859^3 == 777779 (mod 10^6).
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PROG
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(PARI) N=100; Vecrev(digits(lift(chinese(Mod((11/9+O(2^N))^(1/3), 2^N), Mod((11/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
ary = [9]
a = 9
n.times{|i|
b = (a + 7 * (9 * a ** 3 - 11)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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