A337540 Numbers c such that there is a Pythagorean triple (a,b,c) such that (A001414(a), A001414(b), A001414(c)) is also a Pythagorean triple.

5, 289, 86632, 97461, 138125, 176800, 198900, 226304, 254592, 286416, 322218, 342698, 2153437, 6403780, 6602701, 13474900, 13647469, 13952848, 15696954, 17247872, 17329429, 19403856, 20575112, 21829338, 22246250, 23147001, 24134101, 28475200, 31010509, 32034600, 36038925, 36448256, 37328801

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Robert Israel, Pythagorean triples and their sums of prime factors corresponding to the first 41 terms of the sequence.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Index entries related to Pythagorean Triples.

Example

a(1)=5 is in the sequence because (3,4,5) is a Pythagorean triple, whose sums of prime factors with repetition are again (3,4,5).
a(2)=289 is in the sequence because (161, 240, 289) is a Pythagorean triple whose sums of prime factors with repetition are (30, 16, 34), which again is a Pythagorean triple.

Maple

N:= 10^7: # for terms <= N
pyth:= [seq(seq([m^2-n^2, 2*m*n, m^2+n^2], n=1..min(m-1, floor(sqrt(N-m^2)))), m=1..floor(sqrt(N)))]:
filter:= t -> spf(t[3])^2-spf(t[1])^2-spf(t[2])^2=0:
R:= select(filter, pyth):
sort(map(t -> t[3], R));

Crossrefs

Cf. A001414.

Sequence in context: A283569 A252173 A265966 * A354962 A227579 A257045

Adjacent sequences: A337537 A337538 A337539 * A337541 A337542 A337543

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 22 2020

Status

approved