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
KEYWORD
nonn,base
AUTHOR
V. Raman, Sep 01 2012
STATUS
approved