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A375750
Numbers k such that 4*k+1 is the hypotenuse of a primitive Pythagorean triangle with an odd short leg.
5
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
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 13 2024
STATUS
approved