A256455 Numbers that appear at least once in a Pythagorean triple (a, b, b+1).

3, 4, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 24, 25, 27, 29, 31, 33, 35, 37, 39, 40, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 60, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 112, 113

Offset: 1

Author

J. Lowell, Mar 29 2015

Keywords

• nonn

Comments

Includes all odd numbers >= 3 because every odd number a has a Pythagorean triple (a, b, b+1).

Union of A144396 and A046092 (except for 0). - Robert Israel, Mar 29 2015

Examples

			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.
		

Crossrefs

Cf. A144396 (the values of a), A046092 (the values of b), A001844 (the values of b+1).

Programs

Maple

N:= 500: # to get all terms up to N
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