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A210851
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Digits of one of the two 5-adic integers sqrt(-1).
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4
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3, 3, 2, 3, 1, 0, 2, 1, 4, 1, 2, 2, 4, 0, 3, 1, 2, 0, 4, 0, 1, 0, 4, 0, 3, 2, 0, 3, 0, 3, 3, 1, 3, 0, 3, 0, 2, 4, 3, 3, 1, 1, 2, 2, 0, 4, 0, 2, 0, 4, 1, 3, 2, 0, 4, 1, 1, 4, 1, 4, 4, 4, 1, 3, 1, 3, 3, 4, 1, 4, 4, 1, 0, 3, 1, 1, 1, 0, 4, 2, 2, 4, 2, 4, 3, 4, 0, 3, 3, 0, 0, 2, 3, 4, 2, 4, 4, 1, 4, 0
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OFFSET
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0,1
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COMMENTS
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See A048899 for the successive approximations to this 5-adic integer, called -u in a comment on A048898.
The digits of u, the other 5-adic integer sqrt(-1), are given in A210850.
a(n) is the (unique) solution of the linear congruence 2*A048899(n)*a(n) + A210849(n) == 0 (mod 5), n>=1. Therefore only the values 0, 1, 2, 3 and 4 appear. See the Nagell reference given in A210848, eq. (6) on p. 86 adapted to this case. a(0)=3 follows from the formula given below.
If a(n)=0 then A048899(n+1) and A048899(n) coincide.
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LINKS
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Table of n, a(n) for n=0..99.
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FORMULA
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a(n) = (b(n+1) - b(n))/5^n, n>=0, with b(n):=A048899(n) computed from its recurrence. A Maple program for b(n) is given there.
A048899(n+1) = sum(a(k)*5^k, k=0..n), n>=0.
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EXAMPLE
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a(3) = 3 because 2*68*3 + 37 == 0 (mod 5).
A048899(4) = 443 = 3*5^0 + 3*5^1 + 2*5^2 + 3*5^3.
a(5) = 0 because A048899(6) = A048899(5) = 3*5^0 + 3*5^1 + 2*5^2 + 3*5^3 + 1*5^4 = 1068.
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CROSSREFS
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Cf. A048899, A210849, A048898, A210848, A210850.
Sequence in context: A113780 A007515 A014967 * A120992 A129979 A075017
Adjacent sequences: A210848 A210849 A210850 * A210852 A210853 A210854
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Apr 30 2012
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STATUS
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approved
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