The Museum of HP Calculators

HP Forum Archive 17

 Re: Valentine's Day MC: A few modest insights, n! digits - part 3, anyone?Message #1 Posted by Valentin Albillo on 21 Feb 2007, 9:10 a.m. Hi, Gerson: Very nice ! Thanks, Gerson, and Best regards from V.

 Re: Valentine's Day MC: A few modest insights, n! digits - part 3, anyone?Message #2 Posted by Gerson W. Barbosa on 21 Feb 2007, 7:20 p.m.,in response to message #1 by Valentin Albillo Hello Valentin, Quote: Very nice ! 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. ------------------------------------------------ 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.

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