The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086766 a(n) = smallest r where (concatenation of n, r times with itself)*10 + 1 is a prime given by A087403(n), or 0 if no such number exists. 4
 1, 3, 1, 1, 11, 1, 1, 2, 2, 1, 9, 3, 1, 5, 1, 3, 15, 1, 1, 2, 1, 60, 3, 1, 1, 2, 1, 1, 5, 5, 1, 2, 1, 6, 12, 3, 12, 3, 5, 1, 2, 1, 1, 5, 3, 1, 0, 2, 1, 9, 2, 1, 6, 1, 6, 18, 1, 3, 45, 1, 6, 3, 1, 1, 2, 1, 0, 3, 1, 1, 2, 3, 4, 8, 1, 1, 6, 2, 36, 96, 1, 1, 5, 304, 6, 2, 6, 1, 2, 2, 1, 2, 5, 1, 6, 5, 1, 2, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: No term is zero. [Warning: This is known to be wrong, see below. - M. F. Hasler, Jan 08 2015] a(47), a(67), a(100), a(107), a(114) are zero or larger than 1000. - Ray Chandler, Sep 23 2003; edited by M. F. Hasler, Jan 08 2015 a(47) > 10000 or 0. a(67) > 10000 or 0. a(100) > 10000 or 0. a(107) = 2478. a(114) = 1164. See link for more details. - Derek Orr, Oct 02 2014 From Farideh Firoozbakht, Jan 07 2015: (Start) The conjecture is not true and there exist many numbers n such that a(n)=0. Theorem: If m is a positive integer and a(10^m)=r then r+1 divides m+1. Corollary: If p is a prime number then a(10^(p-1))=0 or (10^(p^2)-1)/(10^p-1) is a prime number. By using the theorem and its corollary we can prove that for m = 2, 3, ..., 275 a(10^m)=0. What is the smallest odd prime p, such that (10^(p^2)-1)/(10^p-1) is a prime number (and a(10^(p-1)) could be nonzero)? What is the smallest integer m > 1 such that a(10^m) is nonzero? Conjecture: If n is not of the form 10^m then a(n) is nonzero. M. F. Hasler has checked proofs of the theorem and its corollary. (End) LINKS Derek Orr, Values of a(n) > 1000 for n < 1000 EXAMPLE a(2) = 3, 2221 is a prime but 21 and 221 are composite. PROG (PARI) a(n)=for(k=1, 10^4, if(ispseudoprime((n/(10^#Str(n)-1))*(10^(#Str(n)*k+1)-10)+1), return(k))) vector(46, n, a(n)) \\ Derek Orr, Oct 02 2014 CROSSREFS Cf. A087403. Sequence in context: A060540 A087647 A100265 * A078688 A082466 A120270 Adjacent sequences:  A086763 A086764 A086765 * A086767 A086768 A086769 KEYWORD base,nonn AUTHOR Amarnath Murthy, Sep 10 2003 EXTENSIONS More terms from Ray Chandler, Sep 23 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 13:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)