A099119 Conjectured greatest k such that S(k) = S(k-n), or 0 if no k is known, where S is the Kempner function A002034.

0, 18, 48, 12, 20, 0, 112, 1800, 45, 90, 2475, 48, 5005, 140, 30, 24, 69632, 90, 235144, 60, 750, 4950

Offset

1,2

Comments

Numbers k up to 10^8 have been tested. Tutescu's conjecture is the case n=1.

References

L. Tutescu, "On a Conjecture Concerning the Smarandache Function." Abstracts of Papers Presented to the Amer. Math. Soc. 17, 583, 1996.

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Smarandache Function

Mathematica

(*See A002034 for the Kempner function*) nMax=22; iMax=10^6; iTab=Table[{}, {nMax}]; cTab=Table[0, {nMax}]; a=Table[Kempner[i], {i, nMax+1}]; Do[If[a[[i]]==a[[i-n]], cTab[[n]]++; AppendTo[iTab[[n]], i]], {n, nMax}, {i, n+1, nMax+1}]; Do[a=RotateLeft[a]; a[[nMax+1]]=Kempner[i]; Do[If[a[[nMax+1]]==a[[nMax-n+1]], cTab[[n]]++; AppendTo[iTab[[n]], i]], {n, nMax}], {i, nMax+2, iMax}]; Table[If[iTab[[n]]=={}, 0, Last[iTab[[n]]]], {n, nMax}]

Crossrefs

Cf. A099118 (number of times S(k+n) = S(k)), A099120 (least m such that n = S(k) = S(k+m)).

Sequence in context: A305171 A034132 A218630 * A360589 A105520 A067726

Adjacent sequences: A099116 A099117 A099118 * A099120 A099121 A099122

Keyword

nonn

Author

T. D. Noe, Sep 28 2004

Status

approved