A354381 Primitive elements in A354379, being those not divisible by any previous term.

25, 65, 85, 89, 109, 145, 149, 169, 173, 185, 205, 221, 229, 233, 265, 289, 293, 305, 313, 349, 353, 365, 377, 409, 421, 433, 449, 461, 481, 485, 493, 505, 509, 533, 565, 601, 613, 629, 641, 653, 677, 685, 689, 697, 709, 757, 761, 769, 773, 785, 793, 797, 821, 829, 841, 857, 877, 881, 901, 905

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The primitive Pythagorean triple (39, 80, 89) has all its terms in A009003, and 89 is not divisible by any previous term. Hence 89 is in sequence.

Maple

ishyp:= proc(n) local s; ormap(s -> s mod 4 = 1, numtheory:-factorset(n)) end proc:
filter:= proc(n) local s;
  ormap(s -> ishyp(subs(s, x)) and ishyp(subs(s, y)), [isolve(x^2+y^2=n^2)])
end proc:
R:= []: count:= 0:
for n from 1 while count < 100 do
  if ormap(t -> n mod t = 0, R) then next fi;
  if filter(n) then R:= [op(R), n]; count:= count+1; fi
od:
R; # Robert Israel, Jan 10 2023

Mathematica

ishyp[n_] := AnyTrue[ FactorInteger[n][[All, 1]], Mod[#, 4] == 1 &] ;
filter[n_] := AnyTrue[Solve[x^2 + y^2 == n^2, Integers], ishyp[x /. #] && ishyp[y /. #] &];
R = {}; count = 0;
For[n = 1, count < 100, n++, If[AllTrue[R, Mod[n, #] != 0&], If[filter[n], AppendTo[R, n]; count++]]];
R (* Jean-François Alcover, May 11 2023, after Robert Israel *)

Crossrefs

Cf. A009003, A008846, A020882, A004613, A354379.

Sequence in context: A061970 A159008 A183373 * A306358 A120961 A285579

Adjacent sequences: A354378 A354379 A354380 * A354382 A354383 A354384

Keyword

nonn

Author

Lamine Ngom, May 24 2022

Extensions

Corrected by Robert Israel, Jan 10 2023

Status

approved