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A166079
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Given a row of n pay-phones, all initially unused, how many people can use the pay-phones, assuming (1) each always chooses one of the most distant pay-phones from those in use already, (2) the first person takes a phone at the end, and (3) no people use adjacent phones?
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1
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1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Randall Munroe, Urinal protocol vulnerability
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FORMULA
| a(n) = 1 + 2^floor(lg(n-2) - 1) + max(0, n - 3/2 * 2^floor(lg(n-2)) - 1)
A recurrence is: a(n) = a(m) + a(n-m+1) - 1, with a(1) = a(2) = 1 and a(3)=2, where m = ceiling(n/2). [From John W. Layman (layman(AT)math.vt.edu), Feb 05 2011
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PROG
| (PARI) A000523(n)={my(t=floor(sizedigit(n)*3.32192809)-5); n>>=t; while(n>3, n>>=2; t+=2); if(n==1, t, t+1)}; a(n)={my(t=1<<(A000523(n-2)-1)); max(t+1, n-t-t)}
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CROSSREFS
| A095236, A095912, A095240
Sequence in context: A085578 A135646 A101646 * A080677 A153112 A005350
Adjacent sequences: A166076 A166077 A166078 * A166080 A166081 A166082
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KEYWORD
| easy,nonn
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AUTHOR
| Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 06 2009
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