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

1, 10, 21, 22, 100, 210, 220, 311, 321, 332, 333, 1000, 2100, 2200, 3110, 3210, 3320, 3330, 4111, 4211, 4321, 4331, 4422, 4432, 4443, 4444, 10000, 21000, 22000, 31100, 32100, 33200, 33300, 41110, 42110, 43210, 43310, 44220, 44320, 44430, 44440, 51111, 52111

Offset

1,2

Comments

This sequence contains 1142 terms.

Extension of the autobiographical numbers (or curious numbers) (A046043).

The concatenated numbers from n down to 1 (A000422(1) - A000422(9)): 1, 21, 321, ..., 987654321 are in the sequence.

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.

The powers of 10 (A011557(0)..A011557(9)) are in the sequence.

The numbers of the form a(n)*10^p are also in the sequence.

Links

Michel Lagneau, Table of n, a(n) for n = 1..1142

Example

x0 x1 x2 x3 = 4211 is in the sequence because, for i = 0, 1, 2, 3:
xi > 0 (4 times) => x0 = 4;
xi > 1 (2 times) => x1 = 2;
xi > 2 (1 time) => x2 = 1;
xi > 3 (1 time) => x3 = 1.

Maple

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:

Crossrefs

Cf. A000422, A000461, A011557, A046043.

Sequence in context: A164712 A336558 A338908 * A181450 A364079 A367576

Adjacent sequences: A226192 A226193 A226194 * A226196 A226197 A226198

Keyword

nonn,base,fini,full

Author

Michel Lagneau, May 30 2013

Status

approved