

A137734


a(0)=1. a(n) = ceiling(n/b(n)), where b(n) is the largest value among (a(0),a(1),...,a(n1)).


3



1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Given a(1) = 1, a(n) represents the least number of coins needed to make n cents using coins in the denominations of a(m) for 0 < m < n. For instance, a(10) = 4 because 10 = a(5) + a(5) + a(5) + a(1), and this is the smallest collection of coins with this property.  Alec Jones, Apr 11 2016


LINKS



FORMULA

For all m>=2, a(k) = m if m^2m+1 <= k <= m^2, a(m^2 +1) = m+1, a(k) = m if m^2 +2 <= k <= m^2 +m.


EXAMPLE

The largest value among terms a(0) through a(12) is 4. So a(13) = ceiling(13/4) = 4.


MATHEMATICA

Fold[Append[#1, Ceiling[#2/Max@ #1]] &, {1}, Range@ 100] (* Michael De Vlieger, Oct 16 2017 *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



