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

Author

N. J. A. Sloane, May 13 2007

Keywords

• nonn

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.

Crossrefs

Cf. A006720, A129739, A129740.

Cf. A227199 (primes in this sequence).

Programs

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 *)

Extensions

Order of some of the terms corrected by T. D. Noe, Nov 19 2013