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Write a WP 34S program that displays (and keeps displaying) at least the first 10 correct digits of Brun's Constant, B = 1.902160583104 (the last two digits are uncertain). The maximum number of steps is 10, plus one for each additional digit, up to 12 steps (LBL and END included).

Tip: the following approximation may be used:

B ~ Sqrt(Phi*Sqrt(5.0005)) = 1.90216058363
where
Phi = (sqrt(5) + 1)/2
I have only a 10-step solution:
001 LBL B
002
003
004
005
006
007
008
009
010 END

B --> 1.90216058363

Gerson.


Edited: 27 Dec 2012, 12:09 a.m.

Saved one step immediately:

001: LBL B
002: 5
003: SDR 004
004: RCL+ L
005: [sqrt]
006: # [phi]
007: [times]
008: [sqrt]
009: RTN

Pauli

Quote:
004: RCL+ L

D'oh, missed this obvious one!

Gerson.

And adding a correction term takes three more steps, giving 12 digits on the display although the last is off by a bit:

001: LBL B
002: 5
003: SDR 004
004: RCL+ L
005: [sqrt]
006: # [phi]
007: [times]
008: [sqrt]
009: # 53
010: SDR 11
011: -
012: RTN


- Pauli

10 actual steps for 11 correct digits... this is really compact. #52 instead of #53 might be better.

Gerson.

I didn't fiddle with the correction factor, just interested in the displayed value. Pity the correction value is >255 or an extra digit would have been available for free.

I wouldn't be surprised if a shorter sequence were still possible.


- Pauli

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Another approach, it gets thirteen digits in 12 working steps.

001: LBL B
002: # 216
003: SDR 005
004: #058
005: SDR 008
006: #031
007: SDR 10
008: 4
009: SDR 12
010: [cmplx]+
011: +
012: # 019
013: SDR 001
014: +
015: RTN

- Pauli


Edited: 27 Dec 2012, 1:02 a.m.

Quote:
If only B had made into the WP 34S :-)

Is there anything B is good for beyond pure math?

d:-)

What does it matter? More is always better!


- Pauli

Quote:
What does it matter?
Thanks, that suffices as response - now I know ;-)
Quote:
More is always better!

So you prefer 8.5 over 5.8 on the Richter scale?

([:-)

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Quote:
Well, in 1994 it played an important role in the discovery of the famous Pentium FDIV flaw:

That's of course a serious reason to include it in the WP34s. ;-)

Go on Pauli ... :-)

Franz

Oh yes - we won't take any lower grade challenges, will we? ;-)

Thank you very much for you interest, Paul.

I am sorry if I may have offended someone else's intelligence by posing a "lower grade challenge". Anyway, this was meant to be a simple mini-challenge.

Gerson

Oooh, Gerson, you may have got my message wrong :-? I was just referring to Franz' post and meant we won't introduce a mathematical constant for less reasons than unvealing Intel.

d:-)

I thought the challenge was interesting and I'd still be surprised if a better/shorter solution didn't exist. At the very least it helped take my mind off of the pain of my recent tonsillectomy for a while which was a significant benefit personally.

- Pauli

I hope you'll recover soon.