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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 (list; graph; refs; listen; history; text; internal format)
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)/(1-x)^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[next-coin])

....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

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)