A368086 - OEIS

%I #14 Dec 21 2023 21:23:54

%S 0,1,1,2,2,3,3,4,4,5,-4,4,-3,4,-3,5,-4,7,-6,10,-9,14,-13,19,-18,25,

%T -24,32,-31,40,-38,38,-36,37,-35,37,-35,38,-36,40,-38,43,-41,47,-45,

%U 52,-50,58,-56,65,-62,62,-59,60,-57,59,-56,59,-56,60,-57,62,-59,65,-62,69,-66,74,-71,80,-76

%N The successive sums a(n) + a(n+1) reproduce the decimal expansion of the Champernowne constant.

%H Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/12/champernowne-gamified.html">Champernowne gamified</a>, Personal blog, December 2023.

%e a(1)  + a(2)  =  0 +  1 = 1;

%e a(2)  + a(3)  =  1 +  1 = 2;

%e a(3)  + a(4)  =  1 +  2 = 3;

%e a(4)  + a(5)  =  2 +  2 = 4;

%e a(5)  + a(6)  =  2 +  3 = 5;

%e a(6)  + a(7)  =  3 +  3 = 6;

%e a(7)  + a(8)  =  3 +  4 = 7;

%e a(8)  + a(9)  =  4 +  4 = 8;

%e a(9)  + a(10) =  4 +  5 = 9;

%e a(10) + a(11) =  5 + -4 = 1;

%e a(11) + a(12) = -4 +  4 = 0;

%e a(12) + a(13) =  4 + -3 = 1;

%e a(13) + a(14) = -3 +  4 = 1;

%e a(14) + a(15) =  4 + -3 = 1;

%e a(15) + a(16) = -3 +  5 = 2; etc.

%e The rightmost column reproduces the decimal expansion of the Champernowne constant.

%t s=First@RealDigits[ChampernowneNumber[],10,n=70];

%t a[1]=0;a[n_]:=a[n]=s[[n-1]]-a[n-1];Array[a,n] (* _Giorgos Kalogeropoulos_, Dec 11 2023 *)

%o (Python)

%o from itertools import count, islice

%o def chap():

%o     for k in count(1): yield from list(map(int, str(k)))

%o def agen(): # generator of terms

%o     an = 0

%o     for c in chap():

%o         yield an

%o         an = c - an

%o print(list(islice(agen(), 80))) # _Michael S. Branicky_, Dec 11 2023

%Y Cf. A033307.

%K sign,base,look

%O 1,4

%A _Eric Angelini_ Dec 11 2023