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A060370
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Ratios (p-1)/d, where p is a prime and d is the number of digits of the periodic part of the decimal expansion of 1/p.
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3
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1, 2, 4, 1, 5, 2, 1, 1, 1, 1, 2, 12, 8, 2, 1, 4, 1, 1, 2, 2, 9, 6, 2, 2, 1, 25, 3, 2, 1, 1, 3, 1, 17, 3, 1, 2, 2, 2, 1, 4, 1, 1, 2, 1, 2, 2, 7, 1, 2, 1, 1, 34, 8, 5, 1, 1, 1, 54, 4, 10, 2, 2, 2, 2, 1, 4, 3, 1, 2, 3, 11, 2, 1, 2, 1, 1, 1, 4, 2, 2, 1, 3, 2, 1, 2
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OFFSET
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1,2
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COMMENTS
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The sequence of 2nd, 4th and following terms coincides with A006556, which gives the "number of different cycles of digits in the decimal expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2 or 5".
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LINKS
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FORMULA
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a(n) = (b(n)-1)/c(n), where b(n) and c(n) are the n-th terms of A000040 and A048595 respectively.
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EXAMPLE
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a(13) = 40/5 = 8, since 41 is the 13th prime and the periodic part of 1/41 = 0.02439024390... consists of 5 digits.
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MATHEMATICA
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Join[{1, 2, 4}, Table[p = Prime[n]; (p - 1)/Length[RealDigits[1/p, 10][[1, 1]]], {n, 4, 100}]] (* T. D. Noe, Oct 04 2012 *)
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PROG
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(Python) from sympy import prime, n_order
def A060370(n): return 1 if n == 1 or n == 3 else n_order(10, prime(n))
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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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