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A307620
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Integers x such that [f(0), f(f(0)), ..., f(...f(0)...)] is a permutation of [0, 1, ..., k-1], where k is the number of digits in x and f(a) denotes the 0-based index of the first occurrence of the substring a in x.
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0
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0, 10, 120, 201, 1230, 1302, 2031, 2310, 3012, 3201, 12340, 12403, 13042, 13420, 14023, 14302, 20341, 20413, 23140, 23401, 24103, 24310, 30142, 30421, 32041, 32410, 34012, 34120, 40123, 40312, 42013, 42301, 43021, 43102
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OFFSET
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1,2
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COMMENTS
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Numbers with 21 digits cannot fit every number from 0 to 20 as strings. Hence this sequence cannot have any numbers with 21 digits or more, making it finite.
1918171615141312110 is the largest number in this sequence (see examples).
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LINKS
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EXAMPLE
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Consider x = 40312. f(0) = 1, f(1) = 3, f(3) = 2, f(2) = 4, f(4) = 0 and so we have visited every index of x.
Consider the largest number in this sequence, x = 1918171615141312110. f(0) = 18, f(18) = 2, f(2) = 15, f(15) = 8, f(8) = 3, f(3) = 13, f(13) = 12, f(12) = 14, f(14) = 10, f(10) = 17, f(17) = 4, f(4) = 11, f(11) = 16, f(16) = 6, f(6) = 7, f(7) = 5, f(5) = 9, f(9) = 1, f(1) = 0 and so we have visited every index of x.
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MATHEMATICA
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{{0}}~Join~Array[Block[{k = #, r}, r = Range[0, k]; FromDigits /@ Select[DeleteCases[Permutations[r, {k + 1}], _?(First@ # == 0 &)], With[{w = #}, Union@ Rest@ Nest[Append[#, Position[w, #[[-1]]][[1, 1]] - 1] &, {0}, Length@ w] == r] &]] &, 4] // Flatten (* Michael De Vlieger, Apr 21 2019 *)
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CROSSREFS
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KEYWORD
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nonn,fini,base
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AUTHOR
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STATUS
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approved
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