A252043 a(n) is the concatenation of first n terms of A033307.

1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567891, 12345678910, 123456789101, 1234567891011, 12345678910111, 123456789101112, 1234567891011121, 12345678910111213, 123456789101112131, 1234567891011121314

Offset: 1

Author

José de Jesús Camacho Medina, Dec 15 2014

Keywords

• nonn
• base

Examples

			a(3)=123.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007908 (concatenate 1 through n), A033307.

Programs

Maple

a[0]:= 0;
count:= 0:
for x from 1 to 30 do
  L:= convert(x,base,10);
  for i from 1 to nops(L) do
    count:= count+1;
    a[count]:= a[count-1]*10+L[-i];
  od
od:
seq(a[i],i=1..count); # Robert Israel, Jan 11 2015

Mathematica

b[1] = 1
b[n_] := b[n - 1]*10^(Floor[Log[10, 10n]]) + n
Table[Floor[b[n] /10^(n)], {n, 10, 200}]
Module[{nn=20,ch},ch=RealDigits[ChampernowneNumber[],10,nn][[1]];Table[ FromDigits[ Take[ch,n]],{n,nn}]] (* Harvey P. Dale, Aug 31 2015 *)

Python

from itertools import islice
def bgen(): yield from (c for n in count(1) for c in str(n) )
def agen():
    s, g = "", bgen()
    while True:
        s += next(g); yield int(s)
print(list(islice(agen(), 20))) # Michael S. Branicky, Oct 25 2022

Formula

a(n) = floor(C*10^n) with C the Champernowne constant, 0.123456789101112131415..., A033307.

a(n) = floor(A007908(n)/10^n) For n>=10.

Extensions

Definition corrected by Zak Seidov, Jan 18 2015