

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 backwardsn appears, starting indexing at 0.


3



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
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OFFSET

0,3


LINKS

Chai Wah Wu and 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(10) = 1,
...
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


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



