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Search: id:A099119
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| A099119 |
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Conjectured greatest k such that S(k) = S(k-n), or 0 if no k is known, where S is the Kempner-Smarandache function A002034. |
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+0
4
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| 0, 18, 48, 12, 20, 0, 112, 1800, 45, 90, 2475, 48, 5005, 140, 30, 24, 69632, 90, 235144, 60, 750, 4950
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers k up to 10^8 have been tested. Tutescu's conjecture is the case n=1.
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REFERENCES
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L. Tutescu, "On a Conjecture Concerning the Smarandache Function." Abstracts of Papers Presented to the Amer. Math. Soc. 17, 583, 1996.
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LINKS
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Eric Weisstein's World of Mathematics, Smarandache Function
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MATHEMATICA
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(*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}]; Table[If[iTab[[n]]=={}, 0, Last[iTab[[n]]]], {n, nMax}]
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CROSSREFS
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Cf. A099118 (number of times S(k+n) = S(k)), A099120 (least m such that n = S(k) = S(k+m)).
Sequence in context: A130414 A108642 A034132 this_sequence A105520 A067726 A135189
Adjacent sequences: A099116 A099117 A099118 this_sequence A099120 A099121 A099122
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 28 2004
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