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

Author

Seiichi Manyama, Jun 13 2017

Keywords

• nonn

Comments

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

Examples

			(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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Goebel's Sequence

Crossrefs

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