A288641 Define the sequence {b_n(k)} as the solutions of the recursion (k+1) * b_n(k+1) = b_n(k) * (b_n(k)^(n-1) + k) with b_n(0) = 1. a(n) is the least prime p where p * b_n(p) is not 0 mod p.

43, 89, 97, 251, 19, 239, 37, 79, 83, 239, 31, 431, 19, 79, 23, 827, 43, 173, 31, 103, 179, 73, 19, 431, 193, 101, 53, 811, 47, 1427, 19, 251, 29, 311, 137, 71, 23, 499, 43, 47, 19, 419, 31, 191, 83, 337, 59, 1559, 19, 127, 109, 163, 67, 353, 83, 191, 83, 107

Offset

2,1

Comments

If A108394(n) is a prime, a(n) = A108394(n).

Links

Seiichi Manyama, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Goebel's Sequence

Example

(k+1) * b_2(k+1) = b_2(k) * (b_2(k) + k) with b_2(0) = 1.
b_2(1) == 2, b_2(2) == 3, b_2(3) == 5, ... , b_2(42) == 33 mod 43.
So 43 * b_2(43) == b_2(42) * (b_2(42) + 42) == 24 (> 0) mod 43.

Crossrefs

Cf. A003504 ({b_2(n+1)}), A005166 ({b_3(n)}), A005167 ({b_4(n)}), A108394, A288676.

Sequence in context: A198593 A039526 A108394 * A141924 A122617 A306114

Adjacent sequences: A288638 A288639 A288640 * A288642 A288643 A288644

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2017

Status

approved