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A007615 Primes with unique period length (the periods are given in A007498).
(Formerly M2890)
8
3, 11, 37, 101, 333667, 9091, 9901, 909091, 1111111111111111111, 11111111111111111111111, 99990001, 999999000001, 909090909090909091, 900900900900990990990991, 9999999900000001, 909090909090909090909090909091, 900900900900900900900900900900990990990990990990990990990991 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
REFERENCES
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.
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..98 (terms 1..25 from T. D. Noe; terms 26..31 from Ray Chandler)
C. K. Caldwell, The Prime Glossary, unique prime
FORMULA
a(n) = A061075(A007498(n)). - Max Alekseyev, Oct 16 2010
a(n) = A006530(A019328(A007498(n))). - Ray Chandler, May 10 2017
EXAMPLE
3 is the only prime p such that decimal expansion of 1/p has (nontrivial) period exactly 1.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A061075 A005422 A040017 * A065540 A084171 A192875
KEYWORD
nonn,nice,easy,base
AUTHOR
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)