A190781 - OEIS

A190781

Lucas Aurifeuillian primitive part B of Lucas(10*n - 5).

11, 31, 151, 911, 541, 3641, 272611, 18451, 12760031, 7947701, 767131, 4106261531, 28144128251, 34379101, 120196353941, 823837075741, 51164521, 4215154433351, 2918000731816531, 73998076231, 12462174208709101, 939587136717207031, 3467131047901

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..250

John Brillhart, Peter L. Montgomery and Robert D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), pp. 251-260, S1.

C. K. Caldwell, "Top Twenty" page, Lucas Aurifeuillian primitive part

FORMULA

a(n) = GCD(A061447(10*n-5), A032908(n)*A106729(n-1) + 1).

MATHEMATICA

lst = {1}; n = 23; Do[f = LucasL[k]; Do[f = f/GCD[f, lst[[d]]], {d, Most@Divisors[k]}]; AppendTo[lst, f], {k, 2, 10*n - 5}]; Table[GCD[lst[[5*k]], 5*Fibonacci[k]*(Fibonacci[k] + 1) + 1], {k, 1, 2*n - 1, 2}]

CROSSREFS

Cf. A061447, A190757.

Sequence in context: A181150 A094622 A193645 * A001604 A144727 A002535

Adjacent sequences: A190778 A190779 A190780 * A190782 A190783 A190784

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Dec 29 2012

STATUS

approved