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

0,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Decimal analog of A264596.

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

Sequence in context: A259043 A156207 A061486 * A138470 A325454 A112875

Adjacent sequences: A264597 A264598 A264599 * A264601 A264602 A264603

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 20 2015

Extensions

More terms from Alois P. Heinz, Nov 20 2015

Status

approved