Puzzle: sequence without multiples of 3
09-14-2019, 01:01 AM (This post was last modified: 09-16-2019 08:13 PM by Albert Chan.)
Post: #7
 Albert Chan Senior Member Posts: 1,896 Joined: Jul 2018
RE: Puzzle: sequence without multiples of 3
Hi, Thomas Okken

You got it!

I saw the formula from a book review, The Irrationals, by Julian Havil

The formula itself is trivial, but the procedure to get it can be used for complicated sequences.

Example: for non-squares sequence
Code:
F=n²   1  4  9 16 25 36 49 64 81 n      1  2  3  4  5  6  7  8  9 f=n²-n 0  2  6 12 20 30 42 58 72 f*     1  1  2  2  2  2  3  3  3 n + f* 2  3  5  6  7  8 10 11 12

This assumed f is non-decreasing function.
f* is max k such that f(k) < n, thus we have 2x1, 4x2, 6x3, 8x4 ...

→ f*(n) = floor(√(n) + 0.5)
→ non_squares(n) = n + f* = n + floor(√(n) + 0.5)
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 Messages In This Thread Puzzle: sequence without multiples of 3 - Albert Chan - 09-13-2019, 07:05 PM RE: Puzzle: sequence without multiples of 3 - Voldemar - 09-13-2019, 08:57 PM RE: Puzzle: sequence without multiples of 3 - Voldemar - 09-13-2019, 09:02 PM RE: Puzzle: sequence without multiples of 3 - Albert Chan - 09-13-2019, 09:43 PM RE: Puzzle: sequence without multiples of 3 - Thomas Okken - 09-14-2019, 12:30 AM RE: Puzzle: sequence without multiples of 3 - John Keith - 09-14-2019, 12:54 AM RE: Puzzle: sequence without multiples of 3 - Albert Chan - 09-14-2019 01:01 AM RE: Puzzle: sequence without multiples of 3 - Gerald H - 09-14-2019, 05:37 AM RE: Puzzle: sequence without multiples of 3 - Albert Chan - 09-14-2019, 08:29 AM

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