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A129741
List of primitive prime divisors of the Somos-4 sequence (A006720) in their order of occurrence.
4
2, 3, 7, 23, 59, 157, 11, 139, 8209, 9257, 620297, 983, 4003, 1847, 9803, 1687054711, 1433, 33008447, 83, 101, 113, 51563, 61, 823, 5381, 20117, 6329, 262650531833, 197, 10259, 519606349, 2621, 11887, 136667817691, 13933, 42591667, 564188663, 211, 8802371
OFFSET
1,1
COMMENTS
Read A006720 term-by-term, factorize each term, write down any primes not seen before.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..121 (from the first 49 terms)
G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
MATHEMATICA
a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = (a[n - 1] a[n - 3] + a[n - 2]^2)/a[n - 4]; t = Array[a, 30]; t2 = {}; ps = {}; Do[f = Transpose[FactorInteger[t[[n]]]][[1]]; c = Complement[f, ps]; t2 = Join[t2, c]; ps = Union[ps, c], {n, 4, 30}]; t2 (* T. D. Noe, Nov 19 2013 *)
DeleteDuplicates[DeleteCases[Flatten[FactorInteger[#][[;; , 1]]&/@RecurrenceTable[{a[0]==a[1]== a[2]==a[3]==1, a[n]==(a[n-1]a[n-3]+a[n-2]^2)/a[n-4]}, a, {n, 30}]], 1]] (* Harvey P. Dale, May 25 2024 *)
CROSSREFS
Cf. A227199 (primes in this sequence).
Sequence in context: A376187 A346161 A082449 * A006720 A084710 A088173
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 13 2007
EXTENSIONS
Order of some of the terms corrected by T. D. Noe, Nov 19 2013
STATUS
approved