Conjecture: For n > 1, n divides 2*a(n-1) + 4 if and only if n is prime. - Werner Schulte, Oct 04 2020
For a proof of the above conjecture see Himane. The list of primes p such that p^2 divides (2*a(p-1) + 4) (analog of A007540 - Wilson primes) begins [239, 24049, ...]. - Peter Bala, Nov 06 2024
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Conjecture: For n>1, n divides 2*a(n-1) + 4 if and only if n is prime. - Werner Schulte, Oct 04 2020
From Peter Bala, Nov 06 2024: (Start)
For a proof of the above conjecture see Himane. Similar results include
a) for n >= 3, n divides a(n-2) + 2 if and only if n is prime
b) for n >= 5, n divides 3*a(n-3) + 2 if and only if n is prime
c) for n >= 5, n divides 9*a(n-4) + 1 if and only if n is prime. Cf. A087047.
The list of primes p such that p^2 divides (2*a(p-1) + 4) (analog of A007540 - Wilson primes) begins [239, 24049, ...]. (End)
nonn,easy,nice,changed
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Conjecture: For n>1, n divides 2*a(n-1) + 4 if and only if n is prime. - Werner Schulte, Oct 04 2020
c) for n >= 5, n divides 9*a(n-4) + 1 if and only if n is prime. Cf. A087047. (End)
The list of primes p such that p^2 divides (2*a(p-1) + 4) (analog of A007540 - Wilson primes) begins [239, 24049, ...]. (End)
From Peter Bala, Nov 06 2024: (Start)
For a proof of the above conjecture see Himane. Similar results include
a) for n >= 3, n divides a(n-2) + 2 if and only if n is prime
b) for n >= 5, n divides 3*a(n-3) + 2 if and only if n is prime
c) for n >= 5, n divides 9*a(n-4) + 1 if and only if n is prime. Cf. A087047. (End)
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Djamel Himane, <a href="https://arxiv.org/abs/2404.08646">A simple proof of Werner Schulte's conjecture</a>, arXiv:2404.08646 [math.GM], 2024.
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