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A343103
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a(n) is the sum of the number of times each digit in n (taken with repetition) has appeared in the sequence.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 2, 2, 1, 2, 2, 2, 2, 2, 2, 19, 11, 16, 8, 8, 8, 9, 8, 12, 11, 11, 11, 9, 0, 0, 0, 1, 0, 4, 3, 16, 16, 10, 2, 2, 1, 4, 2, 6, 5, 17, 20, 14, 2, 4, 2, 5, 3, 6, 5, 22, 25, 23, 8, 9, 9, 10, 6, 11, 11, 19, 27, 22, 5, 6, 7, 10, 6, 8, 9, 25, 33, 29, 11, 10, 12, 14, 9
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OFFSET
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0,11
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COMMENTS
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The fixed points > 0 in the first one million terms are 10, 101, 194. It is likely no more exist.
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LINKS
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EXAMPLE
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a(0) to a(9) = 0 as the digits 0 to 9 have not appeared in the sequence.
a(10) = 10 as 1 has appeared zero times and 0 has appeared ten times, thus a(10) = 0 + 10 = 10.
a(11) = 2 as 1 has appeared once in the sequence, and as 1 appears twice in 11, a(11) = 1 + 1 = 2.
a(12) = 2 as 1 has appeared twice and 2 has appeared zero times, thus a(12) = 2 + 0 = 2.
a(20) = 19 as 2 has appeared eight times and 0 has appeared eleven times, thus a(20) = 8 + 11 = 19.
a(22) = 16 as 2 has appeared eight times in the sequence, and as 2 appears twice in 22, a(22) = 8 + 8 = 16.
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MATHEMATICA
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Block[{a = {}, d = ConstantArray[0, 10]}, Do[AppendTo[a, Total@ Map[d[[If[# == 0, 10, #] ]] &, IntegerDigits[i]]]; Set[d, d + DigitCount[a[[i + 1]] ]], {i, 0, 87}]; a] (* Michael De Vlieger, Apr 05 2021 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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