Triangular number AND sum of first m factorials
01-11-2018, 06:29 PM (This post was last modified: 01-11-2018 06:31 PM by Gerson W. Barbosa.)
Post: #13
 Gerson W. Barbosa Senior Member Posts: 1,429 Joined: Dec 2013
RE: Triangular number AND sum of first m factorials
(01-11-2018 10:21 AM)Paul Dale Wrote:  Don't let my proof stop your hunt, you'll be able to wile away many hours looking...

At least I can do it a little more efficiently now :-)

100

« { } SWAP 0 1 ROT 1 SWAP
FOR m m * SWAP OVER + ROT
OVER 8 * 1 + ZSqrt
{ 1 - 2 / + m I→R + }
{ DROP }
IFTE
SWAP ROT
NEXT
DROP2
»

EVAL

-->    { 1 1. 2 2. 17 5. }
(about 17 seconds on the real 50g)

ZSqrt from the LongFloat Library

Yes, that's a consequence of the ever growing number of trailing zeros in factorials and the properties of perfect squares.

Gerson.
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 Messages In This Thread Triangular number AND sum of first m factorials - Joe Horn - 01-09-2018, 04:31 PM RE: Triangular number AND sum of first m factorials - Gerson W. Barbosa - 01-09-2018, 08:53 PM RE: Triangular number AND sum of first m factorials - Dieter - 01-09-2018, 10:19 PM RE: Triangular number AND sum of first m factorials - Gerson W. Barbosa - 01-09-2018, 11:00 PM RE: Triangular number AND sum of first m factorials - Valentin Albillo - 01-09-2018, 10:16 PM RE: Triangular number AND sum of first m factorials - John Keith - 01-09-2018, 11:10 PM RE: Triangular number AND sum of first m factorials - Gerson W. Barbosa - 01-10-2018, 04:03 AM RE: Triangular number AND sum of first m factorials - Joe Horn - 01-10-2018, 04:58 AM RE: Triangular number AND sum of first m factorials - Paul Dale - 01-10-2018, 06:35 AM RE: Triangular number AND sum of first m factorials - Joe Horn - 01-11-2018, 03:01 AM RE: Triangular number AND sum of first m factorials - Paul Dale - 01-11-2018, 10:21 AM RE: Triangular number AND sum of first m factorials - Gerson W. Barbosa - 01-11-2018 06:29 PM RE: Triangular number AND sum of first m factorials - John Keith - 01-11-2018, 10:43 PM RE: Triangular number AND sum of first m factorials - John Keith - 01-11-2018, 10:30 PM RE: Triangular number AND sum of first m factorials - John Cadick - 01-11-2018, 02:22 PM

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