On 04/08/2025 11:16, Ralph Corderoy wrote:
Hi Victor,

    ‘What number is the odd one out, and why: 2 4 6 8 13 19.’
2 is the only even prime.
4 is the only square in the list.
6 is the only perfect number in the list.
8 is the only cube in the list.
Can't think of an argument for 13 or 19 just now.
13 is a happy number, but then so is 19.  :-)

     1² + 3² = 1 + 9 = 10
     1² + 0² = 1 + 0 =  1

     https://en.wikipedia.org/wiki/Happy_number

OEIS does find anything.
https://oeis.org/search?q=2%2C4%2C6%2C8%2C13%2C19&language=english&go=Search

I did come up with a second answer the other night: four is the only one
with the same number of letters in its spelling as its value.

     3  two
   → 4  four
     3  six
     5  eight
     8  thirteen
     8  nineteen

But that's not very mathsy, and why give such an awkward sequence when
a simpler one would do?

     3  one
     3  two
     5  three
   → 4  four
     4  five
     3  six
     5  seven

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.

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