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A188728 Continued fraction of (e+sqrt(16+e^2))/4. 2
1, 1, 7, 1, 46, 8, 30, 1, 5, 4, 2, 6, 3, 2, 5, 1, 1, 1, 3, 50, 1, 3, 1, 1, 3, 1, 45, 1, 1, 1, 4, 1, 1, 2, 8, 2, 35, 2, 1, 27, 6, 112, 1, 113, 16, 1, 11, 1, 1, 6, 1, 12, 1, 3, 2, 15, 1, 2, 1, 1, 5, 1, 16, 2, 2, 2, 1, 10, 1, 43, 1, 13, 1, 6, 1, 4, 1, 2, 1, 1, 1, 6, 1, 8, 8, 1, 6, 3, 3, 17, 3, 1, 27, 1, 11, 1, 1, 1, 1, 1, 1, 9, 7, 2, 1, 5, 5, 7, 6, 2, 1, 5, 1, 2, 1, 5, 57, 8, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A188727 for the origin of the constant.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

[1,1,7,1,46,30,1,5,4,...]= (e+sqrt(16+e^2))/4.

MATHEMATICA

r = e/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]] (* A188727 *)

ContinuedFraction[t, 120] (* A188728 *)

PROG

(PARI) default(realprecision, 100); contfrac((exp(1) + sqrt(16 + exp(2)))/4) \\ G. C. Greubel, Oct 31 2018

(MAGMA) SetDefaultRealField(RealField(100)); ContinuedFraction((Exp(1)  + Sqrt(16 + Exp(2)))/4); // G. C. Greubel, Oct 31 2018

CROSSREFS

Cf. A188640, A188727.

Sequence in context: A027643 A225122 A051931 * A264617 A038267 A027466

Adjacent sequences:  A188725 A188726 A188727 * A188729 A188730 A188731

KEYWORD

nonn,cofr

AUTHOR

Clark Kimberling, Apr 10 2011

STATUS

approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)