The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A181051 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A181051

Incorrect duplicate of A073821.
(history; published version)

#23 by Joerg Arndt at Mon Nov 30 03:57:32 EST 2020

STATUS

reviewed

approved

#22 by Michel Marcus at Mon Nov 30 02:22:18 EST 2020

STATUS

proposed

reviewed

#21 by Joerg Arndt at Mon Nov 30 01:59:25 EST 2020

STATUS

editing

proposed

#20 by Joerg Arndt at Mon Nov 30 01:59:21 EST 2020

NAME

Decimal expansion of the constant whose continued fraction representation is [0; 2, 4, 6, 8, ..., 2*n, ...], i.e., 2/(4+6/(8+10/(12+...) using every even integer.

Incorrect duplicate of A073821.

COMMENTS

Previous name was: Decimal expansion of the constant whose continued fraction representation is [0; 2, 4, 6, 8, ..., 2*n, ...], i.e., 2/(4+6/(8+10/(12+...) using every even integer.

CROSSREFS

See also A113011.

KEYWORD

cons,nonn,more,changed

dead

STATUS

approved

editing

#19 by Joerg Arndt at Mon Nov 30 01:58:12 EST 2020

DATA

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

OFFSET

1,0,1

LINKS

Lucas A. Brown, <a href="/A181051/b181051.txt">Table of n, a(n) for n = 1..1000</a>

EXAMPLE

0.446389965896534507047681795192642669776253147442703859021672487086140473103956401461415197068651827...

MATHEMATICA

BesselI[1, 1]/BesselI[0, 1]

KEYWORD

cons,nonn,changedmore

EXTENSIONS

Corrected and extended by Lucas A. Brown, Nov 30 2020

STATUS

proposed

approved

#18 by Lucas A. Brown at Mon Nov 30 01:53:14 EST 2020

STATUS

editing

proposed

Discussion

Mon Nov 30

01:58

Joerg Arndt: I'll revert and make this "Incorrect duplicate of A073821."

#17 by Lucas A. Brown at Mon Nov 30 01:51:10 EST 2020

LINKS

Lucas A. Brown, <a href="/A181051/b181051.txt">Table of n, a(n) for n = 1..1000</a>

Discussion

Mon Nov 30

01:52

Lucas A. Brown: I don't know what the original author's data was supposed to be, but it didn't match the definition.  Also, this sequence is redundant with A073821.

#16 by Lucas A. Brown at Mon Nov 30 01:50:48 EST 2020

DATA

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

OFFSET

0,1,1

EXAMPLE

0.427038590216724870861404731039564014614151970686518274463899658965345070476817951926426697762531474...

MATHEMATICA

BesselI[1, 1]/BesselI[0, 1]

KEYWORD

cons,nonn,more

EXTENSIONS

Corrected and extended by Lucas A. Brown, Nov 30 2020

STATUS

approved

editing

#15 by Jon E. Schoenfield at Wed Apr 11 23:33:06 EDT 2018

DATA

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

KEYWORD

cons,nonn,changedmore

EXTENSIONS

More terms from Jon E. Schoenfield, Apr 08 2018

STATUS

proposed

approved

#14 by Jon E. Schoenfield at Sun Apr 08 23:58:34 EDT 2018

STATUS

editing

proposed

Discussion

Mon Apr 09

02:59

Michel Marcus: well ... pari contfrac(of this constant) gives me: [0, 2, 2, 1, 12, 1, 1, 2, 126, ... so ??

23:00

Jon E. Schoenfield: Yes, this constant can be expressed as 0 + 1/(2 + 1/(2 + 1/(1 + 1/(12 + 1/(1 + 1/(1 + 1/(2 + 1/(126 + 1/(...))))))))).  It can also be expressed as 2/(4 + 6/(8 + 10/(12 + ...))).  Unfortunately, the existing Name says it's the constant "whose continued fraction representation is [0; 2, 4, 6, 8, ..., 2*n, ...]," and I think many (most?) OEIS readers would take that phrase to mean that it's equivalent to 0 + 1/(2 + 1/(4 + 1/(6 + 1/(8 + 1/(10 + ...))))), which is not correct.  So I believe the existing Name is misleading.

What would you think about changing the Name to the following?

Decimal expansion of the constant that can be expressed as the continued fraction 2/(4+6/(8+10/(12+...))), which uses every even integer.

23:52

G. C. Greubel: The fraction can be generated by f(n) = 4*n + 2*(2*n+1)/f(n+1) for n >=0.

Wed Apr 11

23:29

Jon E. Schoenfield: I have no further suggestions on this sequence.