

A031974


1 repeated prime(n) times.


18



11, 111, 11111, 1111111, 11111111111, 1111111111111, 11111111111111111, 1111111111111111111, 11111111111111111111111, 11111111111111111111111111111, 1111111111111111111111111111111, 1111111111111111111111111111111111111
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Salomaa's first example of an infinite language.  N. J. A. Sloane, Dec 05 2012
If p is a prime and gcd(p,b1)=1, then (b^p1)/(b1) == 1 (mod p); by Fermat's little theorem. For example 1111111 == 1 (mod 7).  Thomas Ordowski, Apr 09 2016


REFERENCES

A. Salomaa, Jewels of Formal Language Theory. Computer Science Press, Rockville, MD, 1981, p. 2.  From N. J. A. Sloane, Dec 05 2012


LINKS

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. 237240
M. Le and K. Wu, The Primes in the Smarandache Unary Sequence, Smarandache Notions Journal, Vol. 9, No. 12. 1998, 9899.
Eric Weisstein's World of Mathematics, Smarandache Sequences


FORMULA

a(n) = A000042(A000040(n)).  Jason Kimberley, Dec 19 2012
a(n) = (10^prime(n)  1)/9.  Vincenzo Librandi, May 29 2014


MAPLE

f:=n>(10^ithprime(n)1)/9; [seq(f(n), n=1..20)]; # N. J. A. Sloane, Dec 05 2012


MATHEMATICA

Table[FromDigits[PadRight[{}, Prime[n], 1]], {n, 15}] (* Harvey P. Dale, Apr 10 2012 *)


PROG

(MAGMA) [(10^p1)/9: p in PrimesUpTo(40)]; // Vincenzo Librandi, May 29 2014


CROSSREFS

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


KEYWORD

nonn,easy,base


AUTHOR

J. Castillo (arp(AT)ciag.com) [Broken email address?]


EXTENSIONS

More terms from Erich Friedman
Corrected and extended by Harvey P. Dale, Apr 10 2012


STATUS

approved



