Re: Valentine's Day MC: A few modest insights, n! digits - part 3, anyone?

[Valentin Albillo]

Hi, Gerson:

Very nice !

Thanks, Gerson, and

Best regards from V.

[Gerson W. Barbosa]

Hello Valentin,

Quote:

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Very nice !

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Thanks, but those two lines of mine are not nearly as nice as the other 17 ones of yours!

Here is my first attempt for the HP-12C. Took more than 5 minutes though :-)

    01  ENTER

    02   LN

    03  LST x

    04   .

    05   5

    06   +

    07   *

    08  x<>y

    09   -

    10   1

    11   1

    12  12/

    13   +

    14   1

    15   0

    16  LN

    17   /

    18   1

    19   +

    20  INTG

    2 <= n <= 100,000,000 (wrong! see update below)

    N = INT(1 + ((n + 1/2)*ln(n) - n + 11/12)/ln(10))

    ln(sqrt(2*pi)) = 0.918938533

             11/12 = 0.916666667

20 steps! Not so bad, considering the 12C lacks pi and common logarithm...

Best regards,

Gerson.

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Update:

Unfortunately, 11/12 is not good enough. The results are one unit less for N=197, 216, 1944, 2512, etc. 34/37 would raise the upper limit to 165534. And 1213/1320 would raise it to 2064172, but in this case it would be better go back to the original formula and start over. Approximating pi as 355/113 (8 steps) would not be of much help...

Edited: 22 Feb 2007, 6:08 p.m.