_T. D. Noe (noe(AT)sspectra.com), _, Sep 28 2004

editing

approved

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

approved

editing

editing

approved

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

approved

editing

E. W. Eric Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheFunction.html">The World of Mathematics: Smarandache Function</a>

nonn,new

nonn

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

nonn,new

nonn

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

nonn,new

nonn

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

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

1,3

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

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

E. W. Weisstein, <a href="http://mathworld.wolfram.com/SmarandacheFunction.html">The World of Mathematics: Smarandache Function</a>

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

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

nonn

T. D. Noe (noe(AT)sspectra.com), Sep 28 2004

approved