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A129738 List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..47.

G. Everest et al., 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

t = Flatten[Table[First/@FactorInteger[(2^n-(-1)^n)/3], {n, 3, 100}]]; t2 = {}; Do[If[! MemberQ[t2, i], AppendTo[t2, i]], {i, t}]; t2 (* Vladimir Joseph Stephan Orlovsky, Feb 05 2012 *)

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: A094747 A300783 A287939 * A271314 A292006 A105603

Adjacent sequences:  A129735 A129736 A129737 * A129739 A129740 A129741

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 13 2007

STATUS

approved

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)