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

3, 5, 11, 7, 43, 17, 19, 31, 683, 13, 2731, 127, 331, 257, 43691, 73, 174763, 41, 5419, 23, 89, 2796203, 241, 251, 4051, 8191, 87211, 29, 113, 59, 3033169, 151, 715827883, 65537, 67, 20857, 131071, 281, 86171, 37, 109, 1777, 25781083, 524287, 22366891, 61681, 83

Offset: 1

Author

N. J. A. Sloane, May 13 2007

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3915
• Graham Everest, Shaun Stevens, Duncan Tamsett and Tom Ward, Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
• K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284.

Crossrefs

Cf. A001045, A049883, A107036, A129733.

Programs

Maple

concat := (a,h)->[op(a),op(sort(convert(h,list)))]:
PPDinOrder := proc(S) local A,H,T,s;
T := {0,1}; A := [];
for s in S do
  H := numtheory[factorset](s) minus T:
  if H <> {} then
    A := concat(A,H);
    T := T union H
  fi
od;
A end:
A129738 := PPDinOrder(A001045);
# Peter Luschny, Jan 04 2011

Mathematica

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