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A007615
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Primes with unique period length (the periods are given in A007498).
(Formerly M2890)
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8
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3, 11, 37, 101, 333667, 9091, 9901, 909091, 1111111111111111111, 11111111111111111111111, 99990001, 999999000001, 909090909090909091, 900900900900990990990991, 9999999900000001, 909090909090909090909090909091, 900900900900900900900900900900990990990990990990990990990991
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OFFSET
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1,1
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COMMENTS
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Additional terms are Phi(n,10)/gcd(n,Phi(n,10)) for the n in A007498, where Phi(n,10) is the n-th cyclotomic polynomial evaluated at 10.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Samuel Yates, Period Lengths of Exactly One or Two Prime Numbers, J. Rec. Math., 18 (1985), 22-24.
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LINKS
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FORMULA
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EXAMPLE
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3 is the only prime p such that decimal expansion of 1/p has (nontrivial) period exactly 1.
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MATHEMATICA
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nmax = 50; periods = Reap[ Do[ p = Cyclotomic[n, 10] / GCD[n, Cyclotomic[n, 10]]; If[ PrimeQ[p], Sow[n]], {n, 1, nmax}]][[2, 1]]; Cyclotomic[#, 10] / GCD[#, Cyclotomic[#, 10]]& /@ periods // Prepend[#, 3]& (* Jean-François Alcover, Mar 28 2013 *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy,base
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AUTHOR
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STATUS
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approved
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