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A233588 Decimal expansion of the continued fraction prime(1) + prime(1)/(prime(2) + prime(2)/(prime(3) + prime(3)/(prime(4) + prime(4)/...))). 14
2, 5, 6, 6, 5, 4, 3, 8, 3, 2, 1, 7, 1, 3, 8, 8, 8, 4, 4, 4, 6, 7, 5, 2, 9, 1, 0, 6, 3, 3, 2, 2, 8, 5, 7, 5, 1, 7, 8, 2, 9, 7, 2, 8, 2, 8, 7, 0, 2, 3, 1, 4, 6, 4, 5, 9, 6, 9, 7, 3, 3, 5, 2, 5, 4, 6, 6, 3, 9, 9, 7, 1, 9, 8, 9, 0, 4, 0, 0, 3, 4, 6, 2, 2, 3, 9, 8, 8, 5, 7, 1, 4, 7, 8, 0, 5, 6, 6, 5, 8, 9, 4, 1, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Given a nondecreasing sequence s(n) of natural numbers (such as, in this case, that of primes A000079), the corresponding continued fraction is bf(s(n)) = a(1) + a(1)/(a(2) + a(2)/(a(3) + a(3)/(...))).
For the inverse of this mapping of nondecreasing sequences of natural numbers into irrational real numbers greater than 1, see A233582.
LINKS
S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001
FORMULA
Equals 2 + 2/(3 + 3/(5 + 5/(7 + 7/(11 + 11/(13 + 13/(17 + ...)))))).
EXAMPLE
2.56654383217138884446752910633228575178297282870231464596973352546639971...
MATHEMATICA
RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ Prime@ Range@ 57], 10, 111][[1]] (* Robert G. Wilson v, May 22 2014 *)
PROG
(PARI) See the link.
CROSSREFS
Sequence in context: A155947 A008294 A019694 * A113975 A035585 A239868
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Jan 02 2014
STATUS
approved

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Last modified March 28 13:19 EDT 2024. Contains 371254 sequences. (Running on oeis4.)