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A040017
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Unique period primes (no other prime has same period as 1/p) in order (periods are given in A051627).
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17
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3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991, 909090909090909090909090909091
(list;
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listen;
history;
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internal format)
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OFFSET
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1,1
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REFERENCES
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J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 324, Pour la Science Paris 2000.
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..46
Chris Caldwell, The Prime Glossary, Unique prime
C. K. Caldwell, "Top Twenty" page, Unique
Chris K. Caldwell and Harvey Dubner, Unique-Period Primes, J. Recreational Math., 29:1 (1998) 43-48.
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Eric Weisstein's World of Mathematics, Unique Prime
Wikipedia, Unique prime
Index entries for sequences related to decimal expansion of 1/n
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EXAMPLE
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The decimal expansion of 1/101 is 0.00990099..., having a period of 4 and it is the only prime with that period.
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MATHEMATICA
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lst = {}; Do[c = Cyclotomic[n, 10]; q = c/GCD[c, n]; If[PrimeQ[q], AppendTo[lst, q]], {n, 62}]; Prepend[Sort[lst], 3] (* Arkadiusz Wesolowski, May 13 2012 *)
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CROSSREFS
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Cf. A007615 (same numbers ordered by period length).
Cf. A007498, A002371, A048595, A006883, A007732, A051626, A051627.
Sequence in context: A243110 A061075 A005422 * A007615 A065540 A084171
Adjacent sequences: A040014 A040015 A040016 * A040018 A040019 A040020
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KEYWORD
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nonn,base,nice
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AUTHOR
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Jud McCranie
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STATUS
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approved
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