A365075 - OEIS

%I #27 Sep 01 2023 04:12:02

%S 5,3,0,6,0,6,0,0,2,0,0,4,0,1,8,0,2,0,5,3,0,2,3,8,0,4,0,1,2,7,5,7,3,6,

%T 0,6,2,5,7,0,3,5,3,6,5,0,8,7,3,3,5,6,0,6,8,6,3,2,0,1,2,3,8,0,9,3,0,1,

%U 9,6,6,4,6,9,5,2,0,6,7,2,0,3,5,0,6,9,2,0,5

%N Decimal expansion of the initial irrational number of Cantor's diagonal argument: the k-th decimal digit of this constant is equal to the k-th decimal digit of A182972(k)/A182973(k).

%D Andrew Hodges, Alan Turing: The Enigma, Princeton University Press, 2014. See p. 153.

%e 0.5306060020040180205392380401375136062570353650803356... whose decimal expansion is given by the decimal digits on the diagonal of the list of rational numbers given by A182972 and A182973:

%e   .5000000000000000000...

%e   .3333333333333333333...

%e   .2500000000000000000...

%e   .6666666666666666667...

%e   .2000000000000000000...

%e   .1666666666666666667...

%e   .4000000000000000000...

%e   .7500000000000000000...

%e   .1428571428571428571...

%e   .6000000000000000000...

%e   .1250000000000000000...

%e   .2857142857142857143...

%e   .8000000000000000000...

%e   .1111111111111111111...

%e   .4285714285714285714...

%e   .1000000000000000000...

%e   ...

%t t1={}; For[n=2, n <= 24, n++, AppendTo[t1, 1/(n-1)]; For[i=2, i <= Floor[(n-1)/2], i++, If[GCD[i, n-i] == 1, AppendTo[t1, i/(n-i)]]]]; (* A182972/A182973 *)

%t a={}; For[i=1, i<Length[t1], i++, AppendTo[a, Mod[Floor[10^i*Part[Rest[t1], i]], 10]]]; a

%o (Python)

%o from itertools import count, islice

%o from math import gcd

%o def A365075_gen(): # generator of terms

%o     c = 1

%o     for n in count(2):

%o         for i in range(1,1+(n-1>>1)):

%o             if gcd(i,n-i)==1:

%o                 c *= 10

%o                 yield (i*c//(n-i))%10

%o A365075_list = list(islice(A365075_gen(),30)) # _Chai Wah Wu_, Aug 28 2023

%Y Cf. A182972, A182973.

%K nonn,base,cons,easy

%O 0,1

%A _Stefano Spezia_, Aug 20 2023

%E Data checked by _Chai Wah Wu_ and corrected by _Stefano Spezia_, Aug 29 2023