A216063 a(n) is the conjectured highest power of n which has no two identical digits in succession.

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

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

Cf. A043096, A216064, A216065, A215236.

Sequence in context: A295787 A308534 A045167 * A114856 A326891 A165019

Adjacent sequences: A216060 A216061 A216062 * A216064 A216065 A216066

Keyword

nonn,base

Author

V. Raman, Sep 01 2012

Status

approved