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

Author

Rick L. Shepherd, May 29 2012

Keywords

• nonn

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.

Examples

			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.
		

Links

• Index entries for sequences related to making change.

Crossrefs

Cf. A212773, A011542, A001300.

Formula

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