A212774 Amounts (in cents) of coins in denominations 1, 5, 10, 25, and 50 (cents) which, when using the minimal number of coins, have equal numbers of all denominations used.

0, 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 20, 22, 25, 26, 30, 31, 35, 36, 40, 41, 50, 51, 55, 56, 60, 61, 65, 66, 75, 76, 80, 81, 85, 86, 90, 91, 100, 102, 120, 122, 150, 153, 200, 204, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950

Offset

1,3

Comments

Nonnegative integers representable as a linear combination of 1, 5, 10, 25, and 50 with nonnegative coefficients, minimal sum of coefficients, and all nonzero coefficients equal.

Includes all nonnegative multiples of 50 and every term > 204 is a multiple of 50.

Unlike A212773, here it is permitted--and necessary--to use a single denomination for some amounts; otherwise, this sequence would be finite.

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to making change.

Formula

a(n) = (n-41)*50 for n >= 46.

Example

a(37) = 91 is a term because the minimal number of coins to equal the amount 91 is five, 91 = 1*1 + 1*5 + 1*10 + 1*25 + 1*50, and there is one of each of the five denominations used.
a(45) = 204 is a term because the minimal number of coins for 204 is eight, 204 = 4*1 + 4*50, and there are four of each of the two denominations used.
Although 12 can be represented as 12*1 or 2*1 + 2*5, requiring 12 or 4 coins and each otherwise meeting the criteria, three (2*1 + 1*10) is the minimal number of coins required and 2 does not equal 1, so 12 is not a term.

Crossrefs

Cf. A212773, A011542, A001300.

Sequence in context: A032902 A018578 A056910 * A131934 A066501 A199191

Adjacent sequences: A212771 A212772 A212773 * A212775 A212776 A212777

Keyword

nonn

Author

Rick L. Shepherd, May 29 2012

Status

approved