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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 (list; graph; refs; listen; history; text; internal format)
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 n-th record in A166079, which is given by the recurrence y(n) = y(m) + y(n-m+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(n-1) + n - 1 if n = 2^k + 2 for some natural number k, a(n) = a(n-1) + 1 otherwise, for n >= 3.

a(n) = n + 2^(1+floor(log_2(n-2))) 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

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Last modified June 19 07:26 EDT 2021. Contains 345126 sequences. (Running on oeis4.)