The On-Line Encyclopedia of Integer Sequences (OEIS)

A191504 revision #23

A191504

Decimal expansion of the number 1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... )))))))))), where coefficients > 1 are the primes.

6, 6, 2, 0, 9, 4, 2, 5, 1, 7, 8, 5, 1, 0, 3, 7, 5, 8, 8, 1, 2, 3, 1, 8, 1, 0, 8, 9, 8, 4, 1, 6, 3, 6, 8, 6, 0, 7, 3, 3, 8, 5, 4, 7, 7, 0, 8, 1, 2, 4, 4, 6, 6, 3, 2, 3, 2, 0, 1, 9, 3, 1, 2, 8, 5, 5, 4, 0, 4, 3, 3, 9, 7, 6, 2, 2, 7, 7, 5, 4, 4, 4, 2, 4, 3, 0, 1, 4, 4, 7, 8, 9, 8, 2, 6, 0, 6, 5, 3, 6, 4, 9, 6, 5, 7, 8, 9, 6, 6, 2, 5, 0, 5, 5, 9, 7, 2, 7, 0, 9, 8, 8, 0, 2, 6, 5, 0, 9, 6, 6, 2, 5, 0, 4, 3, 3, 9, 0, 2, 1, 4, 6, 5, 0, 2, 1, 7, 6, 8, 7, 3, 6, 2, 5, 8, 7, 7, 5, 5, 2, 8, 4, 8, 6, 8, 5, 5, 1, 1, 9, 9, 3, 4, 9, 5, 5, 7, 6, 4, 2, 3, 2, 5, 4, 8, 2, 2, 7, 5

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OFFSET

0,1

COMMENTS

The number can be written 1/(1+s(0)) with s(k)=prime(k)/(1+s(k+1)), prime(0):=1. Asymptotically, s(k) ~ sqrt(prime(k)).

LINKS

Table of n, a(n) for n=0..188.

FORMULA

1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... ))))))))))

EXAMPLE

0.6620942517851037588123181089841636860733854770812446632320193128554043...

MATHEMATICA

N[Fold[#2/(1 + #1) &, 0, Join[Reverse@Prime@Range@180000, {1, 1}]], 111] (* Robert G. Wilson v, Jun 16 2011 *)

PROG

(PARI) default(realprecision, 80); s=sqrt(p=1e6); while(p=precprime(p-1), s=p/(1+s)); eval(vecextract(Vec(Str((1+s)/(2+s))), "3..-2")) \\ - M. F. Hasler, Jun 16 2011.

CROSSREFS

Cf. A191608.

Sequence in context: A098369 A078740 A228708 * A021155 A254245 A218387

Adjacent sequences: A191501 A191502 A191503 * A191505 A191506 A191507

KEYWORD

nonn,cons

AUTHOR

Fabrice Auzanneau, Jun 04 2011

EXTENSIONS

Values corrected upon observation by R. J. Mathar, Jun 16 2011

Corrected and extended by Max Alekseyev, Aug 11 2013

STATUS

approved