A079451 Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.

2, 1, 3, 2, 7, 11, 3, 29, 47, 19, 41, 199, 23, 521, 281, 31, 2207, 3571, 107, 9349, 2161, 211, 307, 461, 1103, 151, 90481, 5779, 14503, 19489, 2521, 3010349, 4481, 9901, 63443, 911, 103681, 54018521, 29134601, 859, 3041, 370248451, 1427, 144481, 967, 541, 275449

Offset: 0

Author

Lekraj Beedassy, Jan 13 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000 (using Blair Kelly's data)
• J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
• Blair Kelly, Factorizations of first 1000 Lucas numbers.

Crossrefs

Cf. A000032 (Lucas numbers), A006530 (greatest prime factor).

Cf. A001606 (indices of prime Lucas numbers <=> where a(n) = A000032(n)), subsequence of A076697 (indices of record values in this sequence).

Cf. A280104 (same for smallest prime factor).

Programs

Magma

[2,1] cat [Maximum(PrimeDivisors(Lucas(n))): n in [2..60]]; // Vincenzo Librandi, Dec 26 2016

Maple

A079451 := proc(n)
        A006530(A000032(n)) ;
end proc:
seq(A079451(n),n=0..30) ; # R. J. Mathar, Oct 26 2013
# second Maple program:
a:= n-> max(ifactors((<<1|1>, <1|0>>^n. <<2, -1>>)[1, 1])[2][..., 1][], 1):
seq(a(n), n=0..46);  # Alois P. Heinz, Aug 04 2025

Mathematica

Join[{2,1},f[n_]:=(FactorInteger@LucasL@n)[[-1,1]];Array[f,60,2]] (* Vincenzo Librandi, Dec 26 2016 *)

PARI

a(n) = my(f = factor(fibonacci(n+1)+fibonacci(n-1))); if (om = #f~, f[om, 1], 1); \\ Michel Marcus, Oct 26 2013

PARI

A079451(n) = A006530(A000032(n)) \\ M. F. Hasler, Apr 10 2025

Python

def A079451(n): return A006530(A000032(n)) # M. F. Hasler, Apr 10 2025

Formula

a(n) = A006530(A000032(n)). - Felix Fröhlich, Dec 26 2016

Extensions

More terms from Michel Marcus, Oct 26 2013

Modified b-file and scripts so that a(1)=1. - David Radcliffe, Aug 03 2025