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

Author

Hugo Pfoertner, Sep 13 2024

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A008846, A081961, A376208.

Programs

PARI

\\ Uses function is_a376208 from A376208
is_a376208(n,1)

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