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A129738 List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence.

%I A129738 #28 Feb 25 2024 01:44:56
%S A129738 3,5,11,7,43,17,19,31,683,13,2731,127,331,257,43691,73,174763,41,5419,
%T A129738 23,89,2796203,241,251,4051,8191,87211,29,113,59,3033169,151,
%U A129738 715827883,65537,67,20857,131071,281,86171,37,109,1777,25781083,524287,22366891,61681,83
%N A129738 List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence.
%C A129738 Read A001045 term-by-term, factorize each term, write down any primes not seen before.
%H A129738 Amiram Eldar, <a href="/A129738/b129738.txt">Table of n, a(n) for n = 1..3915</a>
%H A129738 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 A129738 K. Zsigmondy, <a href="https://doi.org/10.1007%2FBF01692444">Zur Theorie der Potenzreste</a>, Monatsh. Math., 3 (1892), 265-284.
%p A129738 concat := (a,h)->[op(a),op(sort(convert(h,list)))]:
%p A129738 PPDinOrder := proc(S) local A,H,T,s;
%p A129738 T := {0,1}; A := [];
%p A129738 for s in S do
%p A129738   H := numtheory[factorset](s) minus T:
%p A129738   if H <> {} then
%p A129738     A := concat(A,H);
%p A129738     T := T union H
%p A129738   fi
%p A129738 od;
%p A129738 A end:
%p A129738 A129738 := PPDinOrder(A001045);
%p A129738 # _Peter Luschny_, Jan 04 2011
%t A129738 DeleteDuplicates[Flatten[FactorInteger[#][[All,1]]&/@LinearRecurrence[ {1,2},{3,5},50]]](* _Harvey P. Dale_, Apr 14 2020 *)
%Y A129738 Cf. A001045, A049883, A107036, A129733.
%K A129738 nonn
%O A129738 1,1
%A A129738 _N. J. A. Sloane_, May 13 2007