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A225906 Indices of primes whose Wilson quotients are also prime. 3

%I

%S 3,4,5,10,137,216,381

%N Indices of primes whose Wilson quotients are also prime.

%C Is it a coincidence that the terms are alternately odd and even? Is it also a coincidence that the odd terms are all primes (= A225672)?

%H J. Sondow, <a href="http://arxiv.org/abs/1110.3113">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, in Proceedings of CANT 2011, arXiv:1110.3113

%H J. Sondow, <a href="http://link.springer.com/chapter/10.1007%2F978-1-4939-1601-6_17">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.

%F a(n) = A000720(A050299(n+1)).

%e The Wilson quotient of 7 is ((7-1)!+1)/7 = 103, which is prime, and 7 is the 4th prime, so 4 is a member.

%Y Cf. A000720, A007619, A050299, A122696, A225672.

%K nonn

%O 1,1

%A _Jonathan Sondow_, May 20 2013

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Last modified April 9 04:05 EDT 2020. Contains 333343 sequences. (Running on oeis4.)