A064222 a(0) = 0; a(n) = DecimalDigitsSortedDecreasing(a(n-1) + 1) for n > 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 32, 33, 43, 44, 54, 55, 65, 66, 76, 77, 87, 88, 98, 99, 100, 110, 111, 211, 221, 222, 322, 332, 333, 433, 443, 444, 544, 554, 555, 655, 665, 666, 766, 776, 777, 877, 887, 888, 988, 998, 999, 1000, 1100, 1110, 1111, 2111

Offset: 0

Author

Reinhard Zumkeller, Sep 21 2001

Keywords

• nice
• nonn
• base
• look

Comments

a(n) = A004186(a(n-1) + 1). - Reinhard Zumkeller, Oct 31 2007

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004186, A004216, A027468.

Programs

Haskell

a064222 n = a064222_list !! n
a064222_list = iterate (a004186 . (+ 1)) 0
-- Reinhard Zumkeller, Apr 11 2012

Mathematica

NestList[FromDigits[Sort[IntegerDigits[#+1],Greater]]&,0,60] (* Harvey P. Dale, Sep 04 2011 *)

Formula

a(n+1) = (d+0^d)*10^floor(log_10(a(n)+1)) + (1-0^d)*floor(a(n)/10), where d = (a(n)+1) mod 10. - Reinhard Zumkeller, Oct 31 2007

a(n) = (ceiling( (n-G(D(n)-1))/D(n) )*(10^D(n) -1) - 10^( (G(D(n)-1)-n) mod (D(n)) ) + 1)/9, for n>0, where D(n) = floor( (sqrt(8n+1)+3)/6 ) is the number of digits in a(n), and G(k) = A027468(k) = 9*k*(k+1)/2. - Stefan Alexandru Avram, May 24 2023