A262557 Numbers with digits in strictly decreasing order, sorted lexicographically.

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

Offset

1,3

Comments

Original name: "Countdown sequences, allowing gaps."

Only digits 0 through 9 are used. The last term is 9876543210.

Equals A009995, sorted lexicographically. - Reinhard Zumkeller, Oct 14 2015

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

References

Donald S. McDonald, Email message to N. J. A. Sloane, Oct 14 2015.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1023

Formula

a(n) = A009995(A263328(n)); a(A263327(n)) = A009995(n). - Reinhard Zumkeller, Oct 15 2015

Mathematica

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 *)

Prog

(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
-- Reinhard Zumkeller, Oct 14 2015
(PARI) is_A262557 = is_A009995
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

Crossrefs

Cf. A009995, A263327, A263328.

Sequence in context: A173237 A319154 A086068 * A030595 A232590 A094715

Adjacent sequences: A262554 A262555 A262556 * A262558 A262559 A262560

Keyword

nonn,base,fini,full

Author

N. J. A. Sloane, Oct 14 2015

Extensions

New name from M. F. Hasler, Dec 11 2019

Status

approved