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

1,1

Links

Table of n, a(n) for n=1..63.

Example

[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.

Prog

(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
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

Crossrefs

Cf. A000120, A263728.

Sequence in context: A241860 A082884 A193230 * A077036 A076604 A076676

Adjacent sequences: A349117 A349118 A349119 * A349121 A349122 A349123

Keyword

nonn,base,tabf

Author

Ctibor O. Zizka, Nov 08 2021

Status

approved