A113823 Tribonacci analog of A055502.

0, 2, 3, 7, 13, 29, 53, 97, 181, 337, 617, 1151, 2111, 3881, 7151, 13147, 24181, 44483, 81817, 150497, 276817, 509137, 936469, 1722431, 3168097, 5827001, 10717561, 19712669, 36257237, 66687469, 122657377, 225602099, 414946951, 763206467, 1403755531, 2581909003

Offset: 0

Author

Jonathan Vos Post, Jan 23 2006

Keywords

• easy
• nonn

Comments

This is to the tribonacci sequence as A055502 is to the Fibonacci sequence (i.e. least prime greater than the sum of the previous 2 terms in A055502, least prime greater than the sum of the previous 3 terms in this sequence).

The first 9 positive terms are also elements of A089189 but that coincidence breaks down as a(10) = 617 is a prime p, but p-1 = 616 = 2^3 * 7 * 11 is not cubefree.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A055502, A089189.

Programs

Mathematica

a[0] = 0; a[1] = 2; a[2] = 3; a[n_] := a[n] = NextPrime[a[n-1] + a[n-2] + a[n-3]]; Array[a, 40, 0] (* Amiram Eldar, Sep 24 2023 *)

Formula

a(0) = 0, a(1) = 2, for n>2: a(n) = smallest prime > a(n-1)+a(n-2)+a(n-3).

Extensions

More terms from Amiram Eldar, Sep 24 2023