A113239 Prime differences of tribonacci numbers.

2, 3, 5, 11, 17, 23, 31, 37, 43, 79, 193, 491, 503, 653, 883, 1201, 10607, 19009, 19469, 19489, 34963, 35809, 46499, 223273, 223313, 391231, 409817, 410731, 532159, 634061, 754549, 1383769, 1389533, 2552621, 2555753, 3311233, 4477453, 4700621

Offset: 1

Author

Jonathan Vos Post, Oct 19 2005

Keywords

• easy
• nonn

Comments

A113238 is the difference set of tribonacci numbers. A113188-A113194 deal with difference sets of Fibonacci numbers and Lucas numbers and primes in those difference sets.

Examples

			a(1) = 2 because 4 - 2 = 2 where 4 and 2 are tribonacci numbers.
a(2) = 3 because 7 - 4 = 3 where 7 and 4 are tribonacci numbers.
a(3) = 5 because 7 - 2 = 5 where 7 and 2 are tribonacci numbers.
a(4) = 11 because 13 - 2 = 11 where 13 and 2 are tribonacci numbers.
a(5) = 17 because 24 - 7 = 17 where 24 and 7 are tribonacci numbers.
		

Crossrefs

Cf. A000040, A000073, A113188-A113194, A113238.

Programs

Mathematica

Select[Union[Flatten[Differences/@Subsets[Drop[LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 29],2],{2}]]],PrimeQ] (* James C. McMahon, Jun 23 2024 *)

Formula

Intersection of primes A000040 and difference set of tribonacci numbers A113238. Positive prime values of {A000073(i) - A000073(j) such that i>j}.