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

1,1

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.

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 *)

Crossrefs

Cf. A001045, A049883, A107036, A129733.

Sequence in context: A300783 A359115 A287939 * A271314 A292006 A105603

Adjacent sequences: A129735 A129736 A129737 * A129739 A129740 A129741

Keyword

nonn

Author

N. J. A. Sloane, May 13 2007

Status

approved