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A137734 a(0)=1. a(n) = ceiling(n/b(n)), where b(n) is the largest value among (a(0),a(1),...,a(n-1)). 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^2-m+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
Sequence in context: A112310 A350240 A342739 * A366066 A352627 A182210
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Feb 09 2008
STATUS
approved

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Last modified March 1 16:12 EST 2024. Contains 370442 sequences. (Running on oeis4.)