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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).

%I A067995 #20 Dec 04 2023 00:57:58
%S A067995 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,
%T A067995 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,
%U A067995 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
%N 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).
%C A067995 The U.S.A. issued the following unusual denomination coins during the 19th century: 2-cent pieces, 1864-1873; 3-cent pieces, 1851-1889; and 20-cent pieces, 1875-1878.
%D A067995 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)
%H A067995 Ray Chandler, <a href="/A067995/b067995.txt">Table of n, a(n) for n = 1..1000</a>
%H A067995 Jean-Paul Delahaye, <a href="http://www.pourlascience.fr/ewb_pages/a/article-quelles-pieces-pour-faire-l-appoint-20586.php">Quelles pièces pour faire l'appoint ?</a>, French edition of the Scientific American, Pour la Science, N°335, septembre 2005.
%H A067995 Jeffrey Shallit, <a href="http://dx.doi.org/10.1007/BF02984830">What this country needs is an 18c piece</a>, The Mathematical Intelligencer, June 2003, Volume 25, Issue 2, pp 20-23.
%H A067995 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A067995 <a href="/index/Rec#order_101">Index entries for linear recurrences with constant coefficients</a>, 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).
%e A067995 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.
%Y A067995 Cf. A053344, A067996, A067997.
%K A067995 easy,nonn
%O A067995 1,4
%A A067995 _Rick L. Shepherd_, Feb 06 2002