

A185456


Payphone packing sequence.


0



1, 3, 5, 8, 9, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124
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OFFSET

1,2


COMMENTS

Assume that the first person to use a bank of payphones selects one at the end, and all subsequent users select the phone which puts them farthest from the current phone users. U(n) is the smallest number of phones such that n may be used without any two adjacent phones being used.


LINKS

Table of n, a(n) for n=1..60.


FORMULA

a(n) is the index of the nth record in A166079, which is given by the recurrence y(n) = y(m) + y(nm+1)  1, with y(1) = y(2) = 1 and y(3) = 2, where m = ceiling(n/2).  John W. Layman, Feb 05 2011
From Nathaniel Johnston, Apr 12 2011: (Start)
a(n) = a(n1) + n  1 if n = 2^k + 2 for some natural number k, a(n) = a(n1) + 1 otherwise, for n >= 3.
a(n) = n + 2^(1+floor(log_2(n2))) for n >= 3. (End)


EXAMPLE

For 4 phones, only the outer two will be used. For a fifth phone, however, a third person may come along and use the middle phone without any two being adjacent; thus U(3)=5. A seventh phone will not lead to a fourth being used without adjacent people, but an eighth will, hence U(4)=8.


CROSSREFS

Sequence in context: A050094 A137319 A138808 * A308405 A331314 A018804
Adjacent sequences: A185453 A185454 A185455 * A185457 A185458 A185459


KEYWORD

easy,nonn


AUTHOR

Craig B. Daniel, Feb 04 2011


EXTENSIONS

Terms 26,27,...,114 added by John W. Layman, Feb 05 2011
Edited by N. J. A. Sloane, Feb 07 2011
a(51)  a(60) from Nathaniel Johnston, Apr 12 2011


STATUS

approved



