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

Author

Lamine Ngom, May 24 2022

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

Extensions

Corrected by Robert Israel, Jan 10 2023