A129738 - OEIS

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

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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

od;

A end: