A256455 - OEIS

%I #14 Mar 31 2015 00:30:58

%S 3,4,5,7,9,11,12,13,15,17,19,21,23,24,25,27,29,31,33,35,37,39,40,41,

%T 43,45,47,49,51,53,55,57,59,60,61,63,65,67,69,71,73,75,77,79,81,83,84,

%U 85,87,89,91,93,95,97,99,101,103,105,107,109,111,112,113

%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).

%K nonn

%O 1,1

%A _J. Lowell_, Mar 29 2015