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.

11, 60, 61, 19, 180, 181, 25, 312, 313, 35, 612, 613, 41, 840, 841, 47, 1104, 1105, 49, 1200, 1201, 52, 165, 173, 57, 176, 185, 67, 2244, 2245, 97, 4704, 4705, 104, 153, 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

Offset: 1

Author

Ctibor O. Zizka, Nov 08 2021

Keywords

• nonn
• base
• tabf

Examples

			[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.
		

Crossrefs

Cf. A000120, A263728.

Programs

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(aA263728
isok(t) = {my(ht = vecsort(apply(hammingweight, t))); (ht[1]^2 + ht[2]^2 == ht[3]^2) && (gcd(ht)==1);}
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