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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 14:59 EDT 2022. Contains 353957 sequences. (Running on oeis4.)