Triangular number AND sum of first m factorials
01-09-2018, 04:31 PM
Post: #1
 Joe Horn Senior Member Posts: 1,829 Joined: Dec 2013
Triangular number AND sum of first m factorials
153 (my favorite number) is both a triangular number (the sum of the integers 1 through $$n$$; in this case $$n=17$$) as well as the sum of the factorials $$1!$$ through $$m!$$ (in this case $$m=5$$).

The first three natural numbers which have both of those properties are 1, 3 (both trivial) and 153. Find the next number in this sequence. For extra credit, find the mathematical relationship between $$n$$ and $$m$$ for all members of this sequence (which apparently is not yet in OEIS).

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-Joe-
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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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