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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.
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%I #35 Jun 14 2017 07:33:26

%S 43,89,97,251,19,239,37,79,83,239,31,431,19,79,23,827,43,173,31,103,

%T 179,73,19,431,193,101,53,811,47,1427,19,251,29,311,137,71,23,499,43,

%U 47,19,419,31,191,83,337,59,1559,19,127,109,163,67,353,83,191,83,107

%N 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.

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

%H Seiichi Manyama, <a href="/A288641/b288641.txt">Table of n, a(n) for n = 2..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoebelsSequence.html">Goebel's Sequence</a>

%e (k+1) * b_2(k+1) = b_2(k) * (b_2(k) + k) with b_2(0) = 1.

%e b_2(1) == 2, b_2(2) == 3, b_2(3) == 5, ... , b_2(42) == 33 mod 43.

%e So 43 * b_2(43) == b_2(42) * (b_2(42) + 42) == 24 (> 0) mod 43.

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

%K nonn

%O 2,1

%A _Seiichi Manyama_, Jun 13 2017