A113192 Primes that are the difference of two Lucas numbers; primes in A113191.

2, 3, 5, 7, 11, 17, 29, 43, 47, 73, 181, 197, 199, 293, 311, 503, 521, 839, 1361, 2131, 2203, 2207, 3571, 5749, 9349, 13763, 23633, 24469, 24473, 38239, 103483, 103681, 161983, 167759, 271367, 399601, 439081, 439157, 709283, 1692737, 3010349

Offset

1,1

Comments

The difference L(i)-L(j) equals the sum L(j+1)+...+L(i+2).

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Example

The prime 181 is here because it is L(11)-L(6).

Mathematica

Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; lst={}; Do[p=Lucas[n]-Lucas[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, 0, n-2}]; Union[lst]

Crossrefs

Cf. A000032 (Lucas numbers), A001606 (Lucas(n) is prime), A113193 (number of times that Lucas(n)-Lucas(i) is prime for i=0..n-3).

Sequence in context: A356627 A127272 A238528 * A077673 A071255 A062294

Adjacent sequences: A113189 A113190 A113191 * A113193 A113194 A113195

Keyword

nonn

Author

T. D. Noe, Oct 17 2005

Status

approved