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A365075 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).

%I A365075 #27 Sep 01 2023 04:12:02
%S A365075 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 A365075 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 A365075 9,6,6,4,6,9,5,2,0,6,7,2,0,3,5,0,6,9,2,0,5
%N A365075 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 A365075 Andrew Hodges, Alan Turing: The Enigma, Princeton University Press, 2014. See p. 153.
%e A365075 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 A365075   .5000000000000000000...
%e A365075   .3333333333333333333...
%e A365075   .2500000000000000000...
%e A365075   .6666666666666666667...
%e A365075   .2000000000000000000...
%e A365075   .1666666666666666667...
%e A365075   .4000000000000000000...
%e A365075   .7500000000000000000...
%e A365075   .1428571428571428571...
%e A365075   .6000000000000000000...
%e A365075   .1250000000000000000...
%e A365075   .2857142857142857143...
%e A365075   .8000000000000000000...
%e A365075   .1111111111111111111...
%e A365075   .4285714285714285714...
%e A365075   .1000000000000000000...
%e A365075   ...
%t A365075 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 A365075 a={}; For[i=1, i<Length[t1], i++, AppendTo[a, Mod[Floor[10^i*Part[Rest[t1], i]], 10]]]; a
%o A365075 (Python)
%o A365075 from itertools import count, islice
%o A365075 from math import gcd
%o A365075 def A365075_gen(): # generator of terms
%o A365075     c = 1
%o A365075     for n in count(2):
%o A365075         for i in range(1,1+(n-1>>1)):
%o A365075             if gcd(i,n-i)==1:
%o A365075                 c *= 10
%o A365075                 yield (i*c//(n-i))%10
%o A365075 A365075_list = list(islice(A365075_gen(),30)) # _Chai Wah Wu_, Aug 28 2023
%Y A365075 Cf. A182972, A182973.
%K A365075 nonn,base,cons,easy
%O A365075 0,1
%A A365075 _Stefano Spezia_, Aug 20 2023
%E A365075 Data checked by _Chai Wah Wu_ and corrected by _Stefano Spezia_, Aug 29 2023