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A031974
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1 repeated prime(n) times.
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18
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11, 111, 11111, 1111111, 11111111111, 1111111111111, 11111111111111111, 1111111111111111111, 11111111111111111111111, 11111111111111111111111111111, 1111111111111111111111111111111, 1111111111111111111111111111111111111
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OFFSET
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1,1
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COMMENTS
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Salomaa's first example of an infinite language. - N. J. A. Sloane, Dec 05 2012
If p is a prime and gcd(p,b-1)=1, then (b^p-1)/(b-1) == 1 (mod p); by Fermat's little theorem. For example 1111111 == 1 (mod 7). - Thomas Ordowski, Apr 09 2016
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REFERENCES
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A. Salomaa, Jewels of Formal Language Theory. Computer Science Press, Rockville, MD, 1981, p. 2. - From N. J. A. Sloane, Dec 05 2012
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..50
Fanel Iacobescu, Smarandache Partition Type Sequences, in Bulletin of Pure and Applied Sciences, India, Vol. 16E, No. 2, 1997, pp. 237-240
M. Le and K. Wu, The Primes in the Smarandache Unary Sequence, Smarandache Notions Journal, Vol. 9, No. 1-2. 1998, 98-99.
Eric Weisstein's World of Mathematics, Smarandache Sequences
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FORMULA
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a(n) = A000042(A000040(n)). - Jason Kimberley, Dec 19 2012
a(n) = (10^prime(n) - 1)/9. - Vincenzo Librandi, May 29 2014
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MAPLE
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f:=n->(10^ithprime(n)-1)/9; [seq(f(n), n=1..20)]; # N. J. A. Sloane, Dec 05 2012
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MATHEMATICA
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Table[FromDigits[PadRight[{}, Prime[n], 1]], {n, 15}] (* Harvey P. Dale, Apr 10 2012 *)
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PROG
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(MAGMA) [(10^p-1)/9: p in PrimesUpTo(40)]; // Vincenzo Librandi, May 29 2014
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CROSSREFS
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A004022 is the subsequence of primes. - Jeppe Stig Nielsen, Sep 14 2014
Sequence in context: A136982 A083441 A261269 * A117293 A015468 A037842
Adjacent sequences: A031971 A031972 A031973 * A031975 A031976 A031977
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KEYWORD
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nonn,easy,base
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AUTHOR
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J. Castillo (arp(AT)cia-g.com) [Broken email address?]
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EXTENSIONS
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More terms from Erich Friedman
Corrected and extended by Harvey P. Dale, Apr 10 2012
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STATUS
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approved
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