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A212773
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Amounts (in cents) of coins in denominations 1, 5, 10, 25, and 50 (cents) which can consist of equal numbers of coins of all denominations present when two or more denominations are used (or none are used: term 0).
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5
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0, 6, 11, 12, 15, 16, 18, 22, 24, 26, 30, 31, 32, 33, 35, 36, 40, 41, 42, 44, 45, 48, 51, 52, 54, 55, 56, 60, 61, 62, 64, 65, 66, 70, 72, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 93, 96, 99, 102, 104, 105, 108, 110, 112, 114, 120, 121, 122, 123, 124
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OFFSET
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1,2
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COMMENTS
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Nonnegative multiples of each of 6, 11, 15, 16, 26, 31, 35, 40, 41, 51, 56, 61, 65, 76, 81, 85, 86, and 91.
All products of terms are terms.
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LINKS
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EXAMPLE
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4 is not a term because it is not an appropriate multiple. Also 4 = 4*1 cannot be represented with more than one denomination of coin. Similarly 7 is not a term; although 7 = 7*1 = 2*1 + 1*5 does have a representation in terms of two denominations, 1 and 5, there are unequal numbers of each.
a(11) = 30 is a term because it is a multiple of 6. 30 = 5*1 + 5*5 = 2*5 + 2*10 = 1*5 + 1*25, so five coins each of denominations 1 and 5, two each of 5 and 10, or one each of 5 and 25 totals 30.
The term 34924118340711600 (5 times the LCM of the numbers in the first comment, so also divisible by 75) is the smallest which can be expressed in 26 such ways, one for each possible combination of two or more of these five coin denominations. (It also can be expressed as a multiple of each of these five alone of course.)
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PROG
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(PARI)
{c = 0; n = -1; until(c==10000, n++;
if(n%6==0 || n%11==0 || n%15==0 || n%16==0 || n%26==0 ||
n%31==0 || n%35==0 || n%40==0 || n%41==0 || n%51==0 ||
n%56==0 || n%61==0 || n%65==0 || n%76==0 || n%81==0 ||
n%85==0 || n%86==0 || n%91==0,
c++; write("b212773.txt", c, " ", n)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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