This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A009995 Numbers with digits in strictly decreasing order. From the Macaulay expansion of n. 21
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 210, 310, 320, 321, 410, 420, 421, 430, 431, 432, 510, 520, 521, 530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS There are precisely 1023 terms (corresponding to every nonempty subset of {0..9}). A178788(a(n)) = 1. - Reinhard Zumkeller, Jun 30 2010 A193581(a(n)) > 0 for n > 9. - Reinhard Zumkeller, Aug 10 2011 A227362(a(n)) = a(n). - Reinhard Zumkeller, Jul 09 2013 For a fixed natural number r, any natural number n has a unique "Macaulay expansion" n = C(a_r,r)+C(a_{r-1},r-1)+...+C(a_1,1) with a_r > a_{r-1} > ... > a_1 >= 0. If r=10, concatenating the digits a_r, ..., a_1 gives the present sequence. The representation is valid for all n, but the concatenation only makes sense if all the a_i are < 10. - N. J. A. Sloane, Apr 05 2014 a(n) = A262557(A263327(n)); a(A263328(n)) = A262557(n). - Reinhard Zumkeller, Oct 15 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1023 B. Sury, Macaulay Expansion, Amer. Math. Monthly 121 (2014), no. 4, 359--360. MR3183022. [See p. 359. - N. J. A. Sloane, Apr 05 2014] Eric Weisstein's World of Mathematics, Digit. MATHEMATICA Sort@ Flatten@ Table[FromDigits /@ Subsets[ Range[9, 0, -1], {n}], {n, 10}] (* Zak Seidov, May 10 2006 *) PROG (Haskell) import Data.Set (fromList, minView, insert) a009995 n = a009995_list !! n a009995_list = 0 : f (fromList [1..9]) where    f s = case minView s of          Nothing     -> []          Just (m, s') -> m : f (foldl (flip insert) s' \$                               map (10*m +) [0..m `mod` 10 - 1]) -- Reinhard Zumkeller, Aug 10 2011 (PARI) is(n)=fromdigits(vecsort(digits(n), , 12))==n \\ Charles R Greathouse IV, Apr 16 2015 CROSSREFS Cf. A009993. Cf. A262557 (sorted lexicographically), A263327, A263328. Sequence in context: A032865 A032889 A308393 * A190219 A038367 A214958 Adjacent sequences:  A009992 A009993 A009994 * A009996 A009997 A009998 KEYWORD nonn,fini,full,base,look AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 14:33 EDT 2019. Contains 328301 sequences. (Running on oeis4.)