A264600 Let S_n denote the list of decimal numbers 0 to n, written backwards (allowing leading zeros) and arranged in lexicographic order; a(n) = position where backwards-n appears, starting indexing at 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 1, 12

Offset: 0

Author

N. J. A. Sloane, Nov 20 2015

Keywords

• nonn
• base

Examples

			S_0 = [0], so a(0)=0,
...
S_9 = [0,1,2,3,4,5,6,7,8,9], so a(9) = 9,
S_10 = [0,01,1,2,3,4,5,6,7,8,9], so a(10) = 1,
S_11 = [0,01,1,11,2,3,4,5,6,7,8,9], so a(11) = 3,
...
S_20 = [0,01,02,1,11,2,21,3,31,4,41,5,51,6,61,7,71,8,81,9,91], so a(20) = 2, and so on
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 10000 terms from Chai Wah Wu)

Crossrefs

Decimal analog of A264596.

Has same beginning as A061486 but is ultimately different: see A264668.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      irem(n, 10, 'r')*(r+1)+a(r))
    end:
seq(a(n), n=0..101);  # Alois P. Heinz, Nov 20 2015

Mathematica

A264600[0]=0;A264600[n_]:=A264600[n]=Mod[n,10](Floor[n/10]+1)+A264600[Floor[n/10]];Array[A264600,100,0] (* Paolo Xausa, Nov 04 2023, after Alois P. Heinz *)

Python

def A264600(n):
    return sorted(str(i)[::-1] for i in range(n+1)).index(str(n)[::-1]) # Chai Wah Wu, Nov 20 2015

Formula

a(0) = 0, a(10n+m) = a(n) + m*(n+1) for m in {0,...,9}. - Alois P. Heinz, Nov 20 2015

Extensions

More terms from Alois P. Heinz, Nov 20 2015