A113239 - OEIS

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

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

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 *)