A368086 The successive sums a(n) + a(n+1) reproduce the decimal expansion of the Champernowne constant.

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

Offset

1,4

Links

Table of n, a(n) for n=1..71.

Eric Angelini, Champernowne gamified, Personal blog, December 2023.

Example

a(1)  + a(2)  =  0 +  1 = 1;
a(2)  + a(3)  =  1 +  1 = 2;
a(3)  + a(4)  =  1 +  2 = 3;
a(4)  + a(5)  =  2 +  2 = 4;
a(5)  + a(6)  =  2 +  3 = 5;
a(6)  + a(7)  =  3 +  3 = 6;
a(7)  + a(8)  =  3 +  4 = 7;
a(8)  + a(9)  =  4 +  4 = 8;
a(9)  + a(10) =  4 +  5 = 9;
a(10) + a(11) =  5 + -4 = 1;
a(11) + a(12) = -4 +  4 = 0;
a(12) + a(13) =  4 + -3 = 1;
a(13) + a(14) = -3 +  4 = 1;
a(14) + a(15) =  4 + -3 = 1;
a(15) + a(16) = -3 +  5 = 2; etc.
The rightmost column reproduces the decimal expansion of the Champernowne constant.

Mathematica

s=First@RealDigits[ChampernowneNumber[], 10, n=70];
a[1]=0; a[n_]:=a[n]=s[[n-1]]-a[n-1]; Array[a, n] (* Giorgos Kalogeropoulos, Dec 11 2023 *)

Prog

(Python)
from itertools import count, islice
def chap():
    for k in count(1): yield from list(map(int, str(k)))
def agen(): # generator of terms
    an = 0
    for c in chap():
        yield an
        an = c - an
print(list(islice(agen(), 80))) # Michael S. Branicky, Dec 11 2023

Crossrefs

Cf. A033307.

Sequence in context: A187446 A240020 A336430 * A167232 A319468 A137791

Adjacent sequences: A368083 A368084 A368085 * A368087 A368088 A368089

Keyword

sign,base,look

Author

Eric Angelini Dec 11 2023

Status

approved