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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.

%I A264600 #35 Nov 05 2023 09:04:08
%S A264600 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,
%T A264600 29,3,7,11,15,19,23,27,31,35,39,4,9,14,19,24,29,34,39,44,49,5,11,17,
%U A264600 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
%N 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.
%H A264600 Alois P. Heinz, <a href="/A264600/b264600.txt">Table of n, a(n) for n = 0..20000</a> (first 10000 terms from Chai Wah Wu)
%F A264600 a(0) = 0, a(10n+m) = a(n) + m*(n+1) for m in {0,...,9}. - _Alois P. Heinz_, Nov 20 2015
%e A264600 S_0 = [0], so a(0)=0,
%e A264600 ...
%e A264600 S_9 = [0,1,2,3,4,5,6,7,8,9], so a(9) = 9,
%e A264600 S_10 = [0,01,1,2,3,4,5,6,7,8,9], so a(10) = 1,
%e A264600 S_11 = [0,01,1,11,2,3,4,5,6,7,8,9], so a(11) = 3,
%e A264600 ...
%e A264600 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
%p A264600 a:= proc(n) option remember; `if`(n=0, 0,
%p A264600       irem(n, 10, 'r')*(r+1)+a(r))
%p A264600     end:
%p A264600 seq(a(n), n=0..101);  # _Alois P. Heinz_, Nov 20 2015
%t A264600 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_ *)
%o A264600 (Python)
%o A264600 def A264600(n):
%o A264600     return sorted(str(i)[::-1] for i in range(n+1)).index(str(n)[::-1]) # _Chai Wah Wu_, Nov 20 2015
%Y A264600 Decimal analog of A264596.
%Y A264600 Has same beginning as A061486 but is ultimately different: see A264668.
%K A264600 nonn,base
%O A264600 0,3
%A A264600 _N. J. A. Sloane_, Nov 20 2015
%E A264600 More terms from _Alois P. Heinz_, Nov 20 2015