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 Nice sequence (Posted on 2003-08-01)
1,2,6,42,____...

What comes next?

 See The Solution Submitted by Silly Jilly Rating: 2.3333 (6 votes)

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 More solutions from the on-line handbook of integer sequences | Comment 6 of 10 |
Aside from a few more obscure sequences and the ones mentioned already, this also shows up as:

1,2,6,42,618,15018,533418,25935018,1651637418
Sum_{k=1...n} (k!)^2.
Example: a(3)=0!*0!+1!*1!+2!*2!=6.

1,2,6,42,62,102,107,157,232,249,350,384,473,547,637,731,790,920,1005,1031,1042,1063,1109
a(n+1)=a(n) + sum of squares of digits of a(n).
Example: After 1063, since 1^2 + 0^2 + 6^2 + 3^2 = 46 we get 1063+46 = 1109.

1,2,6,42,26,48,92,96,132,20,6,42,26,48,92,96,132,20,6,42,26
Start with 1; add the digits of the previous term and the squares of the digits of the previous term.

1,2,6,42,21,27,405,2304,88263,88263,861993,6100974,80207226
Factorial numbers written backwards.
For example, 5! = 120, backwards it's 021, then drop the now leading zero.

 Posted by Charlie on 2003-08-01 15:07:53

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