cp's OEIS Frontend

A349120 Primitive Pythagorean triples [a, b, c] in lexicographic order with a < b < c such that [w(a), w(b), w(c)] is also a primitive Pythagorean triple, where w(n) is the binary weight of n.

%I A349120 #15 Nov 12 2021 12:26:22
%S A349120 11,60,61,19,180,181,25,312,313,35,612,613,41,840,841,47,1104,1105,49,
%T A349120 1200,1201,52,165,173,57,176,185,67,2244,2245,97,4704,4705,104,153,
%U A349120 185,105,208,233,105,608,617,131,8580,8581,133,156,205,145,408,433,145,10512,10513,165,532,557,181,16380,16381,193,18624,18625
%N A349120 Primitive Pythagorean triples [a, b, c] in lexicographic order with a < b < c such that [w(a), w(b), w(c)] is also a primitive Pythagorean triple, where w(n) is the binary weight of n.
%e A349120 [11, 60, 61] is a primitive Pythagorean triple, and [w(11), w(60), w(61)] = [3, 4, 5] is also a primitive Pythagorean triple, thus 11, 60, and 61 are members.
%o A349120 (PARI) ppt(a) = {my(L=List(), b, c, d, g); fordiv(a^2, d, g=a^2\d; if(d<=g && (d+g)%2==0, c=(d+g)\2; b=g-c; if(a<b && gcd(b, c)==1, listput(L, [a, b, c])))); vecsort(Vec(L), , 2);} \\ A263728
%o A349120 isok(t) = {my(ht = vecsort(apply(hammingweight, t))); (ht[1]^2 + ht[2]^2 == ht[3]^2) && (gcd(ht)==1);}
%o A349120 lista(nn) = {my(list=List()); for (n=1, nn, my(v = ppt(n)); if (#v, for (k=1, #v, if (isok(v[k]), listput(list, v[k]));););); Vec(list);} \\ _Michel Marcus_, Nov 10 2021
%Y A349120 Cf. A000120, A263728.
%K A349120 nonn,base,tabf
%O A349120 1,1
%A A349120 _Ctibor O. Zizka_, Nov 08 2021