A004186 Arrange digits of n in decreasing order.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 22, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 55, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 66, 76, 86, 96, 70, 71, 72

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• look
• easy

Comments

a(A009996(n)) = A009996(n). - Reinhard Zumkeller, Oct 31 2007

If we define "sortable primes" as prime numbers that remain prime when their digits are sorted in decreasing order, then all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. For example, 113 is both sortable and absolute, and 313 is sortable but not absolute since its digits can be permuted to 133 = 7 * 19. - Alonso del Arte, Oct 05 2013

Examples

			a(19) = 91 because the digits of 19 being 1 and 9, arranged in decreasing order they are 9 and 1.
a(20) = 20 because the digits are already in decreasing order.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004185, A004086, A009996, A064222, A194233, A032553, A032554, A028907, A028908.

Programs

Haskell

import Data.List (sort)
a004186 = read . reverse . sort . show :: Integer -> Integer
-- Reinhard Zumkeller, Aug 19 2011

Maple

A004186 := proc(n)
    local dgs;
    convert(n,base,10) ;
    dgs := sort(%) ;
    add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;
end proc:
seq(A004186(n),n=0..20) ; # R. J. Mathar, Jul 26 2015

Mathematica

sortDigitsDown[n_] := FromDigits@ Reverse@ Sort@ IntegerDigits@ n; Array[sortDigitsDown, 73, 0] (* Robert G. Wilson v, Aug 19 2011 *)

PARI

reconstruct(m) = {local(r); r=0; for(i=1,matsize(m)[2],r=r*10+m[i]); r}
A004186(n) = reconstruct(vecsort(digits(n),,4))
\\ Michael B. Porter, Nov 11 2009

PARI

a(n) = fromdigits(vecsort(digits(n), , 4)); \\ Joerg Arndt, Feb 24 2019

Python

def a(n): return int("".join(sorted(str(n), reverse=True)))
print([a(n) for n in range(73)]) # Michael S. Branicky, Feb 21 2021

Formula

n <= a(n) < 10n. - Charles R Greathouse IV, Aug 07 2024

Extensions

More terms from Reinhard Zumkeller, Oct 31 2007