

A258274


The smallest number of cents which cannot be made with fewer than n American coins.


2



1, 2, 3, 4, 9, 19, 44, 94, 194, 294, 394, 494, 594, 694, 794, 894, 994, 1094, 1194, 1294, 1394, 1494, 1594, 1694, 1794, 1894, 1994, 2094, 2194, 2294, 2394, 2494, 2594, 2694, 2794, 2894, 2994
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OFFSET

1,2


COMMENTS

a(n) is the smallest amount (in cents) that cannot be made with fewer than n coins.
The coins included are those in common circulation in the USA: 1¢, 5¢, 10¢, 25¢, 50¢ and $1 (100 cents).


LINKS

Matthew Scroggs, Table of n, a(n) for n = 1..10006


FORMULA

a(n) = 100*n  706 for n >= 8. G.f.: x*(1+4*x^4+5*x^5+15*x^6 +25*x^7 +50*x^8)/(1x)^2.  Robert Israel, May 31 2015


EXAMPLE

The smallest value that requires 5 coins is 9¢ (5¢, 1¢, 1¢, 1¢ and 1¢). Therefore a(5)=9.


PROG

(Python) #
coins = [1, 5, 10, 25, 50, 100]
need = [0]
while True:
....next = len(need)
....n_need = next
....for coin in coins:
........if coin>next:
............break
........n_need = min(n_need, 1+need[nextcoin])
....need.append(n_need)
....if n_need == len(seq):
........print(next)


CROSSREFS

Cf. A258272.
Sequence in context: A220364 A243902 A086865 * A228126 A192988 A280016
Adjacent sequences: A258271 A258272 A258273 * A258275 A258276 A258277


KEYWORD

nonn,easy


AUTHOR

Matthew Scroggs, May 25 2015


STATUS

approved



