Article View: can.rsc.mathsci
Article #23Letters in the name function
From: Willse
Date: Sun, 10 Oct 1999 00:00
Date: Sun, 10 Oct 1999 00:00
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Consider the function (whose domain is members of the set Z*, the set of =
nonnegative integers) defined by
LiN(x)=3D{letters in the formal English name of x}
For example, LiN(8)=3D5, because "eight" has five letters.
LiN(x) for the first few values of {0,1,2,...} are =
{4,3,3,5,4,4,3,5,5,4,3...}.
Prove (or disprove) that, regardless of the initial value of x,
{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4
Travis J. Willse
sal-crumb@geocities.com
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<DIV>All-</DIV>
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<DIV>Consider the function (whose domain is members of the set Z*, the =
set of=20
nonnegative integers) defined by</DIV>
<DIV> </DIV>
<DIV>LiN(x)=3D{letters in the formal English name of x}</DIV>
<DIV> </DIV>
<DIV>For example, LiN(8)=3D5, because "eight" has five letters.</DIV>
<DIV> </DIV>
<DIV>LiN(x) for the first few values of {0,1,2,...} are=20
{4,3,3,5,4,4,3,5,5,4,3...}.</DIV>
<DIV> </DIV>
<DIV>Prove (or disprove) that, regardless of the initial value of =
x,</DIV>
<DIV> </DIV>
<DIV>{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if =
n>1]=3D4</DIV>
<DIV> </DIV>
<DIV>Travis J. Willse</DIV>
<DIV><A =
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A></DIV>=
<DIV> </DIV></BODY></HTML>
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: fd6c7,f6b9d38d2de17c89 X-Google-Attributes: gidfd6c7,public From: "Willse" <gbtt@email.msn.com> Subject: Letters in the name function Date: 1999/10/10 Message-ID: <eCe5Fw6E$GA.211@cpmsnbbsa03> X-Deja-AN: 535263356 References: <e2YeP95E$GA.314@cpmsnbbsa03> X-Priority: 3 Content-Type: multipart/alternative; boundary="----=_NextPart_000_025A_01BF1371.599A9B80" X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2314.1300 X-MSMail-Priority: Normal MIME-Version: 1.0 Newsgroups: can.rsc.mathsci