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A021113 Decimal expansion of 1/109. 5
0, 0, 9, 1, 7, 4, 3, 1, 1, 9, 2, 6, 6, 0, 5, 5, 0, 4, 5, 8, 7, 1, 5, 5, 9, 6, 3, 3, 0, 2, 7, 5, 2, 2, 9, 3, 5, 7, 7, 9, 8, 1, 6, 5, 1, 3, 7, 6, 1, 4, 6, 7, 8, 8, 9, 9, 0, 8, 2, 5, 6, 8, 8, 0, 7, 3, 3, 9, 4, 4, 9, 5, 4, 1, 2, 8, 4, 4, 0, 3, 6, 6, 9, 7, 2, 4, 7, 7, 0, 6, 4, 2, 2, 0, 1, 8, 3, 4, 8, 6, 2, 3, 8, 5, 3, 2, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..107.

"Xochipilli", Le Webinet des curiosit├ęs:les meilleures recettes de Kaprekar (in French)

Guillaume Yoda, Dictionnaire des nombres - 109 (in French)

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

Cf. A018481, A064737.

Sequence in context: A117017 A244861 A058969 * A019948 A154207 A200101

Adjacent sequences:  A021110 A021111 A021112 * A021114 A021115 A021116

KEYWORD

nonn,cons,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 15 16:15 EST 2018. Contains 318150 sequences. (Running on oeis4.)