A129741 List of primitive prime divisors of the Somos-4 sequence (A006720) in their order of occurrence.

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 *)

Crossrefs

Cf. A006720, A129739, A129740.

Cf. A227199 (primes in this sequence).

Sequence in context: A366929 A346161 A082449 * A006720 A084710 A088173

Adjacent sequences: A129738 A129739 A129740 * A129742 A129743 A129744

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