Hi, > > > > ‘What number is the odd one out, and why: 2 4 6 8 13 19.’ ... > Eight, because it is the only one that starts with a vowel. Also not > very mathsy, but it was a pub quiz so may have nothing to do with > maths.
I'm hoping that's not the answer! It occurred to me that I'd searched OEIS wrong: I looked for the sequence 2 4 6 8 13 19 whereas I should have done six searches, one for each sequence of five numbers remaining after dropping each of the six in turn. But that gives many answers. In other words, they're all the odd one out, but only for esoteric reasons. For example, dropping 8 to give 2,4,6,13,19 finds https://oeis.org/A087549: a(1) = 1, a(2) = 1, a(n) = sum of tau(n) previous terms, where tau(n) is the number of divisors of n. 1, 1, 2, 4, 6, 13, 19, 42, 74 My answer on the spot was 19 is the odd one out because summing the digits of all the others, and the digits of the answer until one digit remains, gives even numbers for all of them except 19. 2 → 2 4 → 4 6 → 6 8 → 8 13 → 1 + 3 = 4 19 → 1 + 9 = 10 → 1 + 0 = 1 If I was told the wrong sequence, then another possibility comes from working backwards given 19 - 13 = 6. 19 - 6 = 13 13 - 5 = 8 8 - 4 = 4 4 - 3 = 1 1 But this would need the question to be about 1,4,6,8,13,19, replacing the 2 with a 1. Then 6 is the odd one out. But the lady was very certain of the numbers, so I don't think that's it. So my best answer so far is the digital root. https://en.wikipedia.org/wiki/Digital_root -- Cheers, Ralph. -- Next meeting: Online, Jitsi, Tuesday, 2025-09-02 20:00 Check to whom you are replying Meetings, mailing list, IRC, ... https://dorset.lug.org.uk New thread, don't hijack: mailto:dorset@mailman.lug.org.uk
