cp's OEIS Frontend

A226195 Numbers n = x0 x1 x2...x9 such that xi is the number of digits greater than i in n.

%I A226195 #25 Mar 11 2020 06:07:43
%S A226195 1,10,21,22,100,210,220,311,321,332,333,1000,2100,2200,3110,3210,3320,
%T A226195 3330,4111,4211,4321,4331,4422,4432,4443,4444,10000,21000,22000,31100,
%U A226195 32100,33200,33300,41110,42110,43210,43310,44220,44320,44430,44440,51111,52111
%N A226195 Numbers n = x0 x1 x2...x9 such that xi is the number of digits greater than i in n.
%C A226195 This sequence contains 1142 terms.
%C A226195 Extension of the autobiographical numbers (or curious numbers) (A046043).
%C A226195 The concatenated numbers from n down to 1 (A000422(1) - A000422(9)): 1, 21, 321, ..., 987654321 are in the sequence.
%C A226195 The sequence includes A000461(n) (the n-digit number consisting of all n's) for n=1..9, i.e., 1, 22, 333, 4444, ..., 999999999.
%C A226195 The powers of 10 (A011557(0)..A011557(9)) are in the sequence.
%C A226195 The numbers of the form a(n)*10^p are also in the sequence.
%H A226195 Michel Lagneau, <a href="/A226195/b226195.txt">Table of n, a(n) for n = 1..1142</a>
%e A226195 x0 x1 x2 x3 = 4211 is in the sequence because, for i = 0, 1, 2, 3:
%e A226195 xi > 0 (4 times) => x0 = 4;
%e A226195 xi > 1 (2 times) => x1 = 2;
%e A226195 xi > 2 (1 time) => x2 = 1;
%e A226195 xi > 3 (1 time) => x3 = 1.
%p A226195 T:=array(1..10):for n from 1 to 100000 do:nn:=length(n):for a from 1 to nn do:T[a] :=0:od:x:=convert(n,base,10): for k from 1 to nn do:for i from 1 to nn do: if k-1<x[i] then T[k]:=T[k]+1:else fi:od:od: s:=sum('T[j]*10^(nn-j) ', 'j'=1..nn):if s=n then printf(`%d, `,n):else fi:od:
%Y A226195 Cf. A000422, A000461, A011557, A046043.
%K A226195 nonn,base,fini,full
%O A226195 1,2
%A A226195 _Michel Lagneau_, May 30 2013