

A060802


To weigh from 1 to n, make the heaviest weight as small as possible, under the condition of using fewest pieces of different, single weights; a(n) = weight of the heaviest weight.


1



1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 18, 18, 18, 19, 19, 20, 20, 21
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OFFSET

1,2


COMMENTS

Starting at n = 2^x (x > 2) you get: 3 entries of 2^floor(log_2(x)2)+2, then 2 entries of each subsequent integer until you reach the halfway point between 2^x and 2^(x+1), then 1 entry of each subsequent integer until you reach 2^(x+1)1. Proved (see link).  David Consiglio, Jr., Jan 08 2015


LINKS

David Consiglio, Jr., Table of n, a(n) for n = 1..1024
David Consiglio, Jr., Python that quickly provides weights given the proof by Schoenfield
David Consiglio, Jr., Proof for sequence generation  Schoenfield and Consiglio


FORMULA

After the 8th term:
If 2^x <= n <= (2^x)+2 then a(n) = 2 ^ floor(base2log(x)2)+2 (see A052548)
If (2^x)+2 < n and n+1 < (2^x + 2^x+1)/2 then a(n) and a(n+1) = a(n1)+1
If (2^x+2^x+1)/2 <= n then a(n) = a(n1)+1.  David Consiglio, Jr., Jan 08 2015


EXAMPLE

a(20)=7 because every number from 1 to 20 can be obtained from {1,2,4,6,7}.


CROSSREFS

Sequence in context: A026099 A049727 A260690 * A132073 A087817 A091497
Adjacent sequences: A060799 A060800 A060801 * A060803 A060804 A060805


KEYWORD

nonn


AUTHOR

SenPeng Eu, Apr 27 2001


EXTENSIONS

a(32)a(1024) from David Consiglio, Jr., Jan 08 2015


STATUS

approved



