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Search: id:A111095
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| A111095 |
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Sequence of natural numbers in a non-positional-number-system: the sum of the factorials of the digits provides the related decimal value and index of the element of the sequence. |
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+0
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| 1, 2, 12, 22, 122, 3, 13, 23, 123, 223, 1223, 33, 133, 233, 1233, 2233, 12233, 333, 1333, 2333, 12333, 22333, 122333, 4, 14, 24, 124, 224, 1224, 34, 134, 234, 1234, 2234, 12234, 334, 1334, 2334, 12334, 22334
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OFFSET
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1,2
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COMMENT
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The element a(n) of the sequence is a solution of the following equation: n = sum((floor(a(n)/(10^j))-10*floor(a(n)/(10^(j+1))))!, j = 0..floor(log10(a(n)))); The solution of the equation is not unique, the sequence is generated with the following rules: - each number of the sequence is the solution (principal solution) with the smallest number of digits: a(3) = 12 is the principal solution, a(3) = 111 is a secondary solution; - all the numbers achieved by permutations of the digits of the principal solution are solutions of the equation; the value of the digits of the principal solution does not decrease from left to right: a(3) = 12 is the principal solution, a(3) = 21 is a secondary solution; - 0 is not allowed (typical in not-positional-number-system); I.e. the principal solution is the solution with the smallest decimal value not including digits equal to 0.
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FORMULA
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The element a(n) of the sequence is a solution of the following equation: n = sum((floor(a(n)/(10^j))-10*floor(a(n)/(10^(j+1))))!, j = 0..floor(log10(a(n))));
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EXAMPLE
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a(39) = 12334 because 1! + 2! + 3! + 3! + 4! = 1 + 2 + 6 + 6 + 24 = 39
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CROSSREFS
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Cf. A005096 A108911.
Sequence in context: A017293 A120672 A108960 this_sequence A073211 A094626 A093378
Adjacent sequences: A111092 A111093 A111094 this_sequence A111096 A111097 A111098
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KEYWORD
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nonn,uned
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AUTHOR
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Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Oct 13 2005
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