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

1,1

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.

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A103664 A360053 A129942 * A049553 A049595 A258039

Adjacent sequences: A113236 A113237 A113238 * A113240 A113241 A113242

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 19 2005

Status

approved