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%I #11 Dec 20 2018 13:29:40
%S 4,1,2,1,1,1,2,1,1,2,1,4,1,4,1,9
%N Maximal "digit" in position n from right of numbers in "base American money" representation (A080897).
%C These are the largest numbers of pennies, nickels, dimes, etc. respectively, given in change determined by the usual method of giving as many of the largest denomination as possible before moving to the next smaller, etc. (application of greedy algorithm) in order to use the fewest total coins/bills - and assuming there is always an adequate supply of each denomination.
%C Beyond the 100-dollar denomination explicitly mentioned in A080897, this sequence's terms correspond to 500, 1000, 5000 and 10000-dollar denominations. This sequence considers the 100000-dollar denomination to be the largest (even though it was never designed for public use -- see the U.S. Treasury link for details); hence it doesn't have a corresponding limiting term. If this denomination is disregarded, so should be a(15) = 9.
%C As the four other largest denominations are no longer distributed (although still legal tender), a(11) through a(14) could also be disregarded. In considering a practical, general-purpose change-making algorithm/machine, more helpful might be variations of A080897 and this sequence that ignore infrequently-circulating denominations such as the 50-cent piece and two-dollar bill.
%H U.S. Treasury, <a href="https://www.treasury.gov/resource-center/faqs/Coins/Pages/denominations.aspx">Denominations of Coins</a>
%H U.S. Treasury, <a href="https://www.treasury.gov/resource-center/faqs/Currency/Pages/denominations.aspx">Denominations of Currency</a>
%e a(6) = 2 as, say, A080897(1499) = 102011204, where the "digit" in position 6 (counting from the rightmost being position 0) is 2 (corresponding to two two-dollar bills) -- and no term of A080897 contains a value larger than 2 in position 6. A080897(1499) also exhibits maximal values in positions 0, 2, 3, 4 and 8.
%Y Cf. A080897, A067997 (contains links to other coin denomination info).
%K easy,fini,full,nonn,base
%O 0,1
%A _Rick L. Shepherd_, Jun 08 2005
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