

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
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OFFSET

2,1


COMMENTS

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



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[i1], 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



STATUS

approved



