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).

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

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..88.

Example

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:
  .5000000000000000000...
  .3333333333333333333...
  .2500000000000000000...
  .6666666666666666667...
  .2000000000000000000...
  .1666666666666666667...
  .4000000000000000000...
  .7500000000000000000...
  .1428571428571428571...
  .6000000000000000000...
  .1250000000000000000...
  .2857142857142857143...
  .8000000000000000000...
  .1111111111111111111...
  .4285714285714285714...
  .1000000000000000000...
  ...

Mathematica

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

Prog

(Python)
from itertools import count, islice
from math import gcd
def A365075_gen(): # generator of terms
    c = 1
    for n in count(2):
        for i in range(1, 1+(n-1>>1)):
            if gcd(i, n-i)==1:
                c *= 10
                yield (i*c//(n-i))%10
A365075_list = list(islice(A365075_gen(), 30)) # Chai Wah Wu, Aug 28 2023

Crossrefs

Cf. A182972, A182973.

Sequence in context: A374172 A350550 A232225 * A200126 A065469 A249522

Adjacent sequences: A365072 A365073 A365074 * A365076 A365077 A365078

Keyword

nonn,base,cons,easy

Author

Stefano Spezia, Aug 20 2023

Extensions

Data checked by Chai Wah Wu and corrected by Stefano Spezia, Aug 29 2023

Status

approved