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A225906 Indices of primes whose Wilson quotients are also prime. 3
3, 4, 5, 10, 137, 216, 381 (list; graph; refs; listen; history; text; internal format)
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 * A329524 A319067 A224503

Adjacent sequences:  A225903 A225904 A225905 * A225907 A225908 A225909

KEYWORD

nonn

AUTHOR

Jonathan Sondow, May 20 2013

STATUS

approved

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Last modified February 27 07:02 EST 2020. Contains 332299 sequences. (Running on oeis4.)