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

1,1

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

Links

Table of n, a(n) for n=1..63.

Example

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.

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

Crossrefs

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

Sequence in context: A141259 A349165 A047501 * A035242 A190941 A284752

Adjacent sequences: A256452 A256453 A256454 * A256456 A256457 A256458

Keyword

nonn

Author

J. Lowell, Mar 29 2015

Status

approved