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A129738
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List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence.
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2
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Read A001045 term-by-term, factorize each term, write down any primes not seen before.
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REFERENCES
| G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 11 4 (No. 5, 2007), 417-431.
K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284.
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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
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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 (* From Vladimir Joseph Stephan Orlovsky, Feb 05 2012 *)
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CROSSREFS
| Cf. A001045, A049883, A107036, A129733.
Sequence in context: A145398 A087322 A094747 * A105603 A170835 A122133
Adjacent sequences: A129735 A129736 A129737 * A129739 A129740 A129741
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 13 2007
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