A375750 Numbers k such that 4*k+1 is the hypotenuse of a primitive Pythagorean triangle with an odd short leg.

1, 3, 6, 10, 15, 16, 21, 22, 24, 28, 36, 37, 39, 42, 45, 46, 48, 51, 55, 58, 66, 67, 69, 72, 76, 78, 79, 84, 88, 91, 94, 97, 105, 106, 108, 111, 115, 120, 121, 123, 126, 130, 135, 136, 139, 142, 153, 154, 157, 163, 168, 171, 172, 174, 177, 181, 186, 190, 192, 193

Offset

1,2

Comments

Sorted distinct values of ({A081961} - 1)/4.

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Prog

(Python)
from math import gcd, isqrt
test_all_k_upto   = 193
A375750, x, limit = set(), 2, test_all_k_upto * 4 + 1
while x**2 + (lowY := isqrt(2*x**2)-x)**2 < limit:
   for y in range(min(x-1, (yy:=isqrt(limit - x**2))-(yy%2 == x%2)), lowY, -2):
       if gcd(x, y) == 1: A375750.add(((x**2 + y**2) - 1) // 4)
   x += 1
print(A375750:=sorted(A375750)) # Karl-Heinz Hofmann, Sep 17 2024
(PARI) \\ Uses function is_a376208 from A376208
is_a376208(n, 1)

Crossrefs

Cf. A008846, A081961, A376208.

Sequence in context: A074374 A109804 A231672 * A120993 A194458 A083266

Adjacent sequences: A375747 A375748 A375749 * A375751 A375752 A375753

Keyword

nonn

Author

Hugo Pfoertner, Sep 13 2024

Status

approved