%N Numbers that appear at least once in a Pythagorean triple (a, b, b+1).
%C Includes all odd numbers >= 3 because every odd number a has a Pythagorean triple (a, b, b+1).
%C Union of A144396 and A046092 (except for 0). - _Robert Israel_, Mar 29 2015
%e 12 qualifies because it's part of (5, 12, 13). 8 doesn't qualify because no Pythagorean triple of the form (a, b, b+1) has 8 in it; in every triple of this kind, b is the only even number, and a in the triple (a, 8, 9) would be the square root of 17, which is not an integer.
%p N:= 500: # to get all terms up to N
%p sort([seq(2*i+1, i=1 .. floor((N-1)/2)), seq(2*j*(j+1), j = 1 .. floor((sqrt(1+2*N)-1)/2))]); # _Robert Israel_, Mar 29 2015
%Y Cf. A144396 (the values of a), A046092 (the values of b), A001844 (the values of b+1).
%A _J. Lowell_, Mar 29 2015