A031974 1 repeated prime(n) times.

11, 111, 11111, 1111111, 11111111111, 1111111111111, 11111111111111111, 1111111111111111111, 11111111111111111111111, 11111111111111111111111111111, 1111111111111111111111111111111, 1111111111111111111111111111111111111

Offset: 1

Author

J. Castillo (arp(AT)cia-g.com) [Broken email address?]

Keywords

• nonn
• easy
• base

Comments

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

Also Mersenne numbers (A001348) written in binary. - Kritsada Moomuang, May 13 2025

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. 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

Crossrefs

A004022 is the subsequence of primes. - Jeppe Stig Nielsen, Sep 14 2014

Cf. A001348.

Programs

Magma

[(10^p-1)/9: p in PrimesUpTo(40)]; // 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 *)

Formula

a(n) = A000042(A000040(n)). - Jason Kimberley, Dec 19 2012

a(n) = (10^prime(n) - 1)/9. - Vincenzo Librandi, May 29 2014

Extensions

More terms from Erich Friedman

Corrected and extended by Harvey P. Dale, Apr 10 2012