OFFSET
0,3
COMMENTS
From Paul Curtz, Feb 23 2012: (Start)
The sequence of digits is periodic with period length 108. A feature of the period reading from the least significant digit back to the most significant digit is (see the blogspot link and A064737) that it "contains" the single-digit of every Fibonacci subsequence if the digits are added with carry of the previous sum. A064737 starts with the A000045 sequence, and then 5+8 = (1)3, 3+8+1=(1)2. "Every" Fibonacci sequence means (as illustrated in the blog) that one could also start from seeds like 6 and 7, or 7 and 8.
Similar observations are made for the digits of 1/89 in A021093, but following a Fibonacci pattern while reading in the other direction, starting with the most significant digits.
The frequency distribution of the digits 0 to 9 among the 108 digits (which sum to 486) of the period is well-balanced: 10, 11, 11, 11, 11, 11, 11, 11, 11, 10. If one sums over each 2nd, each 3rd, each 6th, each 9th or each 18th digit of the period, one gets 1/2, 1/3, 1/6, 1/9 and 1/18 of 486; again a feature of balance in the digits. There is a half-period in the sense that a(n) + a(n+54) = 9. (End)
LINKS
"Xochipilli", Le Webinet des curiosités:les meilleures recettes de Kaprekar (in French)
Guillaume Yoda, Dictionnaire des nombres - 109 (in French)
FORMULA
Equals Sum_{k>=1} (-1)^(k+1) * Fibonacci(k)/10^(k+1). - Amiram Eldar, Feb 05 2022
EXAMPLE
0.00917431192660550458715596330275229357798165137614...
MATHEMATICA
RealDigits[1/109, 10, 100][[1]] (* Alonso del Arte, Feb 11 2012 *)
PROG
(PARI) 1/109. \\ Charles R Greathouse IV, Feb 13 2012
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved