A109601 A puzzle sequence: you are asked to find the next three terms. I know nothing more about it.

87, 711, 43, 269, 65, 555, 39, 421, 17

Offset

0,1

Comments

William Maness, Oct 24 2011, observes that so far the terms are all odd numbers and the numbers of digits is alternately 2 and 3. Sequence is likely from a book of math puzzles for grade school.

The answer to the puzzle could be 209, 28, 343. The sequence can be bisected into a 2-digit sequence b = {87, 43, 65, 39, 17, b(6)} and a 3-digit sequence c = {711, 269, 555, 421, c(5), c(6)}. Note that the first 3 terms in sequence b satisfy: b(1) - b(3) = b(3) - b(2) = 22. Assuming that the last 3 terms follow the similar pattern, b(4) - b(6) = b(6) - b(5) = x, we have b(6) = 28 and x = 11 = 22/2. In sequence c, c(1) - c(3) = 156 and c(3) - c(2) = 286 = 156 + 2*b(3). Similarly, c(4) - c(6) = 156/2 and c(6) - c(5) = 156/2 + 2*b(6), which means c(6) = c(4) - 156/2 = 343 and c(5) = 209. - Ya-Ping Lu, Oct 21 2025

Links

Table of n, a(n) for n=0..8.

Crossrefs

Sequence in context: A359341 A297509 A259510 * A297723 A061625 A220055

Adjacent sequences: A109598 A109599 A109600 * A109602 A109603 A109604

Keyword

nonn,unkn,base,dumb

Author

N. J. A. Sloane, following an email message from Lisa Chu, Jul 25 2005

Extensions

Comment from William Maness added by David Applegate, Oct 24 2011 and edited by N. J. A. Sloane

Status

approved