This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099118 #10 Feb 16 2025 08:32:54
%S A099118 0,1,2,2,3,0,9,3,2,5,18,2,28,9,2,1,53,2,79,5,10,23
%N A099118 Conjectured number of times that S(k+n) = S(k), where S is the Kempner function A002034.
%C A099118 Numbers k up to 10^8 have been tested. Tutescu's conjecture is the case n=1.
%D A099118 L. Tutescu, "On a Conjecture Concerning the Smarandache Function." Abstracts of Papers Presented to the Amer. Math. Soc. 17, 583, 1996.
%H A099118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheFunction.html">Smarandache Function</a>
%t A099118 (*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
%Y A099118 Cf. A099119 (greatest k such that S(k) = S(k-n)), A099120 (least m such that n = S(k) = S(k+m)).
%K A099118 nonn
%O A099118 1,3
%A A099118 _T. D. Noe_, Sep 28 2004