A129738
List of primitive prime divisors of the Jacobsthal numbers A001045 in their order of occurrence.
Original entry on oeis.org
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
- 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.
-
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
-
DeleteDuplicates[Flatten[FactorInteger[#][[All,1]]&/@LinearRecurrence[ {1,2},{3,5},50]]](* Harvey P. Dale, Apr 14 2020 *)
A129736
Primes of the form 4^k - 3^k.
Original entry on oeis.org
7, 37, 14197, 17050729021, 332306984815842876487217260305275077
Offset: 1
- Muniru A Asiru, Table of n, a(n) for n = 1..13
- Bogley, William A.; Williams, Gerald Efficient finite groups arising in the study of relative asphericity. Math. Z. 284, No. 1-2, 507-535 (2016).
- 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.
-
Filtered(List([1..100], n -> 4^n-3^n), IsPrime); # Muniru A Asiru, Feb 09 2018
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[a: n in [0..300] | IsPrime(a) where a is 4^n-3^n]; // Vincenzo Librandi, Nov 23 2010
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select(isprime, [seq(4^n - 3^n, n=0..100)]); # Muniru A Asiru, Feb 09 2018
-
fQ[n_] := If[PrimeQ[4^n - 3^n], 4^n - 3^n, Nothing]; Array[fQ, 300] (* Robert G. Wilson v, Feb 12 2018 *)
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lista(nn) = for(k=1, nn, if(isprime(p=4^k-3^k), print1(p", "))) \\ Altug Alkan, Mar 03 2018
A129735
List of primitive prime divisors of the numbers (4^n-1)/3 (A002450) in their order of occurrence.
Original entry on oeis.org
5, 3, 7, 17, 11, 31, 13, 43, 127, 257, 19, 73, 41, 23, 89, 683, 241, 2731, 8191, 29, 113, 151, 331, 65537, 43691, 131071, 37, 109, 174763, 524287, 61681, 337, 5419, 397, 2113, 47, 178481, 2796203, 97, 673, 251, 601, 1801, 4051, 53, 157, 1613, 87211, 262657, 15790321, 59, 233, 1103, 2089, 3033169, 61, 1321, 715827883, 2147483647
Offset: 1
The primes grouped according to successive terms of A002450, courtesy of _James R. Buddenhagen_:
[5], [3, 7], [17], [11, 31], [13], [43, 127], [257], [19, 73], [41], [23, 89, 683], [241], [2731, 8191], [29, 113], [151, 331], [65537], [43691, 131071], [37, 109], [174763, 524287], [61681], [337, 5419], [397, 2113], [47, 178481, 2796203], [97, 673], [251, 601, 1801, 4051], [53, 157, 1613], [87211, 262657], [15790321], [59, 233, 1103, 2089, 3033169], [61, 1321], [715827883, 2147483647], ...
- James R. Buddenhagen, List giving n followed by primitive prime divisors of (4^n-1)/3 for n=1..70
- G. Everest, S. Stevens, D. Tamsett and T. Ward, Primes Generated by Recurrence Sequences, 2006.
- G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
- Wikipedia, Zsigmondy's theorem
- K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284.
A129737
List of primitive prime divisors of the numbers 4^n-3^n (A005061) in their order of occurrence.
Original entry on oeis.org
7, 37, 5, 11, 71, 13, 14197, 337, 6553, 181, 23, 174659, 193, 131, 500111, 379, 61, 601, 17, 4241, 17050729021, 19, 163, 10814953, 25309, 8861, 8352709, 727, 859, 47, 44483, 17389, 1933, 51361, 1440528320401, 313, 31357, 36174709, 2053, 29, 376853, 59, 349
Offset: 1
A129734
List of primitive prime divisors of the numbers 3^n-2^n (A001047) in their order of occurrence.
Original entry on oeis.org
5, 19, 13, 211, 7, 29, 71, 97, 1009, 11, 23, 331, 61, 53, 29927, 463, 3571, 17, 401, 129009091, 577, 1559, 745181, 4621, 43, 6217, 35839, 47, 2002867877, 5521, 101, 39756701, 79, 4057, 397760329, 369181, 68629840493971, 31, 241, 617671248800299, 3041, 14177
Offset: 1
- Amiram Eldar, Table of n, a(n) for n = 1..1893
- 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.
Showing 1-5 of 5 results.
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