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A021893
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Decimal expansion of 1/889.
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0
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0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5
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OFFSET
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0,5
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COMMENTS
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Sum_{j>=0} tribonacci(j) / 10^(j+1).
Generalization (since tribonacci(j+3) =
tribonacci(j+2) + tribonacci(j+1) + tribonacci(j)):
1/889 = Sum_{j>=0} tribonacci(j) / 10^(j+1), (this sequence)
1/989899 = Sum_{j>=0} tribonacci(j) / 100^(j+1),
1/998998999 = Sum_{j>=0} tribonacci(j) / 1000^(j+1),
1/999899989999 = Sum_{j>=0} tribonacci(j) / 10000^(j+1),
...
1 / ((10^k)^3 - (10^k)^2 - (10^k)^1 - (10^k)^0) = 1 / (10^(3k) - 10^(2k) - 10^k - 1) = Sum_{j>=0} tribonacci(j) / (10^k)^(j+1), k >= 1.
Sum_{j>=0} 111^j / 1000^(j+1).
Generalization (since 111^(j+1) = 111*111^j):
1/889 = Sum_{j>=0} 111^j / 1000^(j+1), (this sequence)
1/9889 = Sum_{j>=0} 111^j / 10000^(j+1),
1/99889 = Sum_{j>=0} 111^j / 100000^(j+1),
1/999889 = Sum_{j>=0} 111^j / 1000000^(j+1),
...
1 / ((10^k)^1 - 111*(10^k)^0) = 1 / (10^k - 111) = Sum_{j>=0} 111^j / (10^k)^(j+1), k >= 3. (End)
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
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FORMULA
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a(n) = a(n-1) - a(n-21) + a(n-22) for n > 21.
G.f.: (-x^21 - 8*x^20 + 8*x^18 - 6*x^17 + 7*x^16 - 4*x^15 + 2*x^14 - 2*x^13 - 3*x^12 + 7*x^11 - 6*x^10 + 6*x^9 - 4*x^8 + 3*x^7 - 4*x^6 - 2*x^5 - x^4 - x^2)/(x^22 - x^21 + x - 1). (End)
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MATHEMATICA
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Join[{0, 0}, RealDigits[1/889, 10, 120][[1]]] (* or *) PadRight[{}, 120, {0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1}] (* Harvey P. Dale, Dec 02 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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