A004186 - OEIS

%I #49 Aug 07 2024 10:36:28

%S 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,

%T 62,72,82,92,30,31,32,33,43,53,63,73,83,93,40,41,42,43,44,54,64,74,84,

%U 94,50,51,52,53,54,55,65,75,85,95,60,61,62,63,64,65,66,76,86,96,70,71,72

%N Arrange digits of n in decreasing order.

%C a(A009996(n)) = A009996(n). - _Reinhard Zumkeller_, Oct 31 2007

%C 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

%H R. Zumkeller, <a href="/A004186/b004186.txt">Table of n, a(n) for n = 0..10000</a>

%F n <= a(n) < 10n. - _Charles R Greathouse IV_, Aug 07 2024

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

%e a(20) = 20 because the digits are already in decreasing order.

%p A004186 := proc(n)

%p     local dgs;

%p     convert(n,base,10) ;

%p     dgs := sort(%) ;

%p     add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;

%p end proc:

%p seq(A004186(n),n=0..20) ; # _R. J. Mathar_, Jul 26 2015

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

%o (PARI)

%o reconstruct(m) = {local(r); r=0; for(i=1,matsize(m)[2],r=r*10+m[i]); r}

%o A004186(n) = reconstruct(vecsort(digits(n),,4))

%o \\ _Michael B. Porter_, Nov 11 2009

%o (PARI) a(n) = fromdigits(vecsort(digits(n), , 4)); \\ _Joerg Arndt_, Feb 24 2019

%o (Haskell)

%o import Data.List (sort)

%o a004186 = read . reverse . sort . show :: Integer -> Integer

%o -- _Reinhard Zumkeller_, Aug 19 2011

%o (Python)

%o def a(n): return int("".join(sorted(str(n), reverse=True)))

%o print([a(n) for n in range(73)]) # _Michael S. Branicky_, Feb 21 2021

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

%K nonn,base,look,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Reinhard Zumkeller_, Oct 31 2007