A225906 Indices of primes whose Wilson quotients are also prime.

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

Offset

1,1

Comments

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)?

Links

Table of n, a(n) for n=1..7.

J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113

J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A123820 A261903 A133320 * A332790 A329524 A319067

Adjacent sequences: A225903 A225904 A225905 * A225907 A225908 A225909

Keyword

nonn

Author

Jonathan Sondow, May 20 2013

Status

approved