The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216063 a(n) is the conjectured highest power of n which has no two identical digits in succession. 10
126, 133, 63, 32, 26, 27, 42, 33, 1, 16, 15, 11, 76, 15, 26, 19, 18, 8, 1, 45, 38, 19, 12, 16, 30, 22, 11, 21, 1, 16, 16, 11, 12, 11, 13, 10, 23, 10, 1, 22, 19, 6, 18, 25, 23, 11, 10, 6, 1, 6, 8, 20, 14, 17, 11, 13, 14, 13, 1, 15, 14, 17, 21, 16, 16, 9, 4, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Contribution from Charles R Greathouse IV, Sep 17 2012: (Start)
a(n) = 0 for infinitely many n; such n have positive density in this sequence. Question: are such n of density 1?
A naive heuristic suggests that there are infinitely many n such that a(n) = 6 but only finitely many a(n) such that a(n) > 6. This suggests a weaker conjecture: this sequence is bounded. (end)
LINKS
V. Raman and T. D. Noe, Table of n, a(n) for n = 2..1000 (V. Raman computed the terms 2 to 99)
EXAMPLE
3^133 = 2865014852390475710679572105323242035759805416923029389510561523 which has no two adjacent identical digits.
MATHEMATICA
Table[mx = 0; Do[If[! MemberQ[Differences[IntegerDigits[n^k]], 0], mx = k], {k, 1000}]; mx, {n, 2, 100}] (* T. D. Noe, Sep 17 2012 *)
PROG
(PARI) isA043096(n)=my(v=digits(n)); for(i=2, #v, if(v[i]==v[i-1], return(0))); 1
a(n)=my(best=0); if(n==14, 76, for(k=1, max(9, 94\sqrt(log(n))), if(isA043096(n^k), best=k)); best ) \\ (conjectural) Charles R Greathouse IV, Sep 17 2012
CROSSREFS
Sequence in context: A295787 A308534 A045167 * A114856 A326891 A165019
KEYWORD
nonn,base
AUTHOR
V. Raman, Sep 01 2012
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 07:02 EDT 2024. Contains 372772 sequences. (Running on oeis4.)