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%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
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