A067995 Minimal number of coins needed to pay exactly n cents using coins of sizes 1, 2, 3, 5, 10, 20, 25, 50, 100 cents (all historical U.S.A. coinage from 1 to 100 cents).
1, 1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 4, 5, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 1, 2, 2, 2, 3, 2
Offset: 1
Examples
a(69) = 5 because to pay exactly 69 cents at least 5 coins are needed: e.g. 1 of 50 cents, 1 of 10 cents, 1 of 5 cents and 2 of 2 cents.
References
- R. S. Yeoman, A Guide Book of United States Coins, Ed. Kenneth Bressett, 53rd Edition (2000). New York: St. Martin's Press, 1999. pp. 104-106, 135. (also known as The Official Red Book of United States Coins)
Links
- Ray Chandler, Table of n, a(n) for n = 1..1000
- Jean-Paul Delahaye, Quelles pièces pour faire l'appoint ?, French edition of the Scientific American, Pour la Science, N°335, septembre 2005.
- Jeffrey Shallit, What this country needs is an 18c piece, The Mathematical Intelligencer, June 2003, Volume 25, Issue 2, pp 20-23.
- Index entries for sequences related to making change.
- Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
Comments