A099118 Conjectured number of times that S(k+n) = S(k), where S is the Kempner function A002034.

0, 1, 2, 2, 3, 0, 9, 3, 2, 5, 18, 2, 28, 9, 2, 1, 53, 2, 79, 5, 10, 23

Offset: 1

Author

T. D. Noe, Sep 28 2004

Keywords

• nonn

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

• Eric Weisstein's World of Mathematics, Smarandache Function

Crossrefs

Cf. A099119 (greatest k such that S(k) = S(k-n)), A099120 (least m such that n = S(k) = S(k+m)).

Programs

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}]; cTab