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
Keywords
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
Programs
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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
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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