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A060282
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Periodic part of decimal expansion of reciprocal of n-th prime (leading 0's omitted).
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4
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0, 3, 0, 142857, 9, 76923, 588235294117647, 52631578947368421, 434782608695652173913, 344827586206896551724137931, 32258064516129, 27, 2439, 23255813953488372093, 212765957446808510638297872340425531914893617
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = floor(10^A002371(n)/prime(n)).
a(n) = 0 if and only if n = 1 or 3, corresponding to the primes 2 and 5, which are factors of 10. - Alonso del Arte, Apr 03 2020
ceiling(log_10(a(n))) = prime(n) - 1 if prime(n) is a full reptend prime (A001913). - Alonso del Arte, Apr 14 2020
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EXAMPLE
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1/7 = 0.142857142..., so a(4) = 142857.
1/11 = 0.09090909..., so a(5) = 9.
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MATHEMATICA
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primePer[1] = primePer[3] = 0; primePer[n_] := FromDigits[(d = RealDigits[1/Prime[n]])[[1, 1]]] * 10^d[[2]]; Array[ primePer, 15] (* Amiram Eldar, Apr 28 2020 *)
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PROG
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(PARI) f(n)=if(n<4, n==2, znorder(Mod(10, prime(n)))) \\ A002371
for(n=1, 100, print1(floor(10^f(n)/prime(n)), ", "))
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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