A252043 - OEIS

%I #62 Oct 25 2022 10:19:54

%S 1,12,123,1234,12345,123456,1234567,12345678,123456789,1234567891,

%T 12345678910,123456789101,1234567891011,12345678910111,

%U 123456789101112,1234567891011121,12345678910111213,123456789101112131,1234567891011121314

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

%H Harvey P. Dale, <a href="/A252043/b252043.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%e a(3)=123.

%p a[0]:= 0;

%p count:= 0:

%p for x from 1 to 30 do

%p   L:= convert(x,base,10);

%p   for i from 1 to nops(L) do

%p     count:= count+1;

%p     a[count]:= a[count-1]*10+L[-i];

%p   od

%p od:

%p seq(a[i],i=1..count); # _Robert Israel_, Jan 11 2015

%t b[1] = 1

%t b[n_] := b[n - 1]*10^(Floor[Log[10, 10n]]) + n

%t Table[Floor[b[n] /10^(n)], {n, 10, 200}]

%t Module[{nn=20,ch},ch=RealDigits[ChampernowneNumber[],10,nn][[1]];Table[ FromDigits[ Take[ch,n]],{n,nn}]] (* _Harvey P. Dale_, Aug 31 2015 *)

%o (Python)

%o from itertools import islice

%o def bgen(): yield from (c for n in count(1) for c in str(n) )

%o def agen():

%o     s, g = "", bgen()

%o     while True:

%o         s += next(g); yield int(s)

%o print(list(islice(agen(), 20))) # _Michael S. Branicky_, Oct 25 2022

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

%K nonn,base

%O 1,2

%A _José de Jesús Camacho Medina_, Dec 15 2014

%E Definition corrected by _Zak Seidov_, Jan 18 2015