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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.

%I A375750 #40 Sep 27 2024 23:20:43
%S A375750 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 A375750 76,78,79,84,88,91,94,97,105,106,108,111,115,120,121,123,126,130,135,
%U A375750 136,139,142,153,154,157,163,168,171,172,174,177,181,186,190,192,193
%N A375750 Numbers k such that 4*k+1 is the hypotenuse of a primitive Pythagorean triangle with an odd short leg.
%C A375750 Sorted distinct values of ({A081961} - 1)/4.
%H A375750 Karl-Heinz Hofmann, <a href="/A375750/b375750.txt">Table of n, a(n) for n = 1..10000</a>
%o A375750 (Python)
%o A375750 from math import gcd, isqrt
%o A375750 test_all_k_upto   = 193
%o A375750 A375750, x, limit = set(), 2, test_all_k_upto * 4 + 1
%o A375750 while x**2 + (lowY := isqrt(2*x**2)-x)**2 < limit:
%o A375750    for y in range(min(x-1,(yy:=isqrt(limit - x**2))-(yy%2 == x%2)), lowY,-2):
%o A375750        if gcd(x,y) == 1: A375750.add(((x**2 + y**2) - 1) // 4)
%o A375750    x += 1
%o A375750 print(A375750:=sorted(A375750)) # _Karl-Heinz Hofmann_, Sep 17 2024
%o A375750 (PARI) \\ Uses function is_a376208 from A376208
%o A375750 is_a376208(n,1)
%Y A375750 Cf. A008846, A081961, A376208.
%K A375750 nonn
%O A375750 1,2
%A A375750 _Hugo Pfoertner_, Sep 13 2024