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A262557
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Numbers with digits in strictly decreasing order, sorted lexicographically.
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6
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0, 1, 10, 2, 20, 21, 210, 3, 30, 31, 310, 32, 320, 321, 3210, 4, 40, 41, 410, 42, 420, 421, 4210, 43, 430, 431, 4310, 432, 4320, 4321, 43210, 5, 50, 51, 510, 52, 520, 521, 5210, 53, 530, 531, 5310, 532, 5320, 5321, 53210, 54, 540, 541, 5410, 542, 5420, 5421
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Original name: "Countdown sequences, allowing gaps."
Only digits 0 through 9 are used. The last term is 9876543210.
There are 2^k terms starting with digit k >= 0, they start at index 2^k. The countdown sequences, i.e., digits of the n-th term, are given in rows of A272011. - M. F. Hasler, Dec 11 2019
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REFERENCES
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Donald S. McDonald, Email message to N. J. A. Sloane, Oct 14 2015.
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LINKS
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FORMULA
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MATHEMATICA
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A262557[n_] := FromDigits[BitLength[n] - Flatten[Position[IntegerDigits[n, 2], 1]]]; Array[A262557, 100] (* or *)
A262557full = Rest[Map[FromDigits, LexicographicSort[Subsets[Range[9, 0, -1]]]]] (* Paolo Xausa, Feb 13 2024 *)
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PROG
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(Haskell)
a262557 n = a262557_list !! (n-1)
a262557_list = 0 : f [[0]] where
f xss = if x < 9 then (map (read . concatMap show) zss) ++ f zss else []
where zss = (map (z :) $ map tail xss) ++ (map (z :) xss)
z = x + 1; x = head $ head xss
apply( A262557(n)=fromdigits(Vecrev(vecextract([0..exponent(n+!n)], n))), [1..99])
# A262557=concat(apply(x(i)=concat(vector(i%10+1, j, if(j>1, x(i*10+j-2), i))), [0..9])) \\ M. F. Hasler, Dec 11 2019
(Python)
from itertools import combinations
afull = list(map(int, sorted("".join(c) for i in range(1, 11) for c in combinations("9876543210", i)))) # Michael S. Branicky, Feb 13 2024
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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