%I #28 Feb 25 2024 01:44:56

%S 3,5,11,7,43,17,19,31,683,13,2731,127,331,257,43691,73,174763,41,5419,

%T 23,89,2796203,241,251,4051,8191,87211,29,113,59,3033169,151,

%U 715827883,65537,67,20857,131071,281,86171,37,109,1777,25781083,524287,22366891,61681,83

%N List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence.

%C Read A001045 term-by-term, factorize each term, write down any primes not seen before.

%H Amiram Eldar, <a href="/A129738/b129738.txt">Table of n, a(n) for n = 1..3915</a>

%H Graham Everest, Shaun Stevens, Duncan Tamsett and Tom Ward, <a href="http://www.jstor.org/stable/27642221">Primes generated by recurrence sequences</a>, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

%H K. Zsigmondy, <a href="https://doi.org/10.1007%2FBF01692444">Zur Theorie der Potenzreste</a>, Monatsh. Math., 3 (1892), 265-284.

%p concat := (a,h)->[op(a),op(sort(convert(h,list)))]:

%p PPDinOrder := proc(S) local A,H,T,s;

%p T := {0,1}; A := [];

%p for s in S do

%p H := numtheory[factorset](s) minus T:

%p if H <> {} then

%p A := concat(A,H);

%p T := T union H

%p fi

%p od;

%p A end:

%p A129738 := PPDinOrder(A001045);

%p # _Peter Luschny_, Jan 04 2011

%t DeleteDuplicates[Flatten[FactorInteger[#][[All,1]]&/@LinearRecurrence[ {1,2},{3,5},50]]](* _Harvey P. Dale_, Apr 14 2020 *)

%Y Cf. A001045, A049883, A107036, A129733.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 13 2007