A375750 - OEIS

%I #40 Sep 27 2024 23:20:43

%S 1,3,6,10,15,16,21,22,24,28,36,37,39,42,45,46,48,51,55,58,66,67,69,72,

%T 76,78,79,84,88,91,94,97,105,106,108,111,115,120,121,123,126,130,135,

%U 136,139,142,153,154,157,163,168,171,172,174,177,181,186,190,192,193

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

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

%H Karl-Heinz Hofmann, <a href="/A375750/b375750.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from math import gcd, isqrt

%o test_all_k_upto   = 193

%o A375750, x, limit = set(), 2, test_all_k_upto * 4 + 1

%o while x**2 + (lowY := isqrt(2*x**2)-x)**2 < limit:

%o    for y in range(min(x-1,(yy:=isqrt(limit - x**2))-(yy%2 == x%2)), lowY,-2):

%o        if gcd(x,y) == 1: A375750.add(((x**2 + y**2) - 1) // 4)

%o    x += 1

%o print(A375750:=sorted(A375750)) # _Karl-Heinz Hofmann_, Sep 17 2024

%o (PARI) \\ Uses function is_a376208 from A376208

%o is_a376208(n,1)

%Y Cf. A008846, A081961, A376208.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Sep 13 2024