A094965 - OEIS

A094965

A continued fraction transformation of e.

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

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OFFSET

1,1

COMMENTS

The terms of the continued fraction representation of this constant (2.126671411...) are the decimal digits of e.

When trying to recover the digits of e from this continued fraction, one gets 2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 13, 5, ... whereas e is 2.718281828459045...; recovered "digits" (sometimes greater than 9) that do not match the actual decimal digits of e occur around places where the actual digits include a 0. E.g., the "904" substring in the actual digits of e results in a recovered "digit" of 9+4 = 13. - Michel Marcus and Jon E. Schoenfield, Mar 16 2018

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

2.126671411...

MATHEMATICA

RealDigits[ FromContinuedFraction[ RealDigits[E, 10, 125][[1]]], 10, 111][[1]]

CROSSREFS

Cf. A001113.

Sequence in context: A285030 A281781 A351317 * A025277 A248100 A153896

Adjacent sequences: A094962 A094963 A094964 * A094966 A094967 A094968

KEYWORD

cons,easy,nonn,base

AUTHOR

Robert G. Wilson v, May 26 2004

STATUS

approved