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A286181 Lesser of Wilson's pseudo-twin primes: primes p such that p! == 1 (mod q), where q=A151800(p) is the next prime after p, and q-p>2. 4
7841, 594278556271608991, 4259842839142238791410741595983041626644087433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By Wilson's theorem, p! == 1 (mod p+2) whenever p,p+2 are twin primes. This sequence and A286208 concern consecutive primes p,q satisfying p! = 1 (mod q), where d = q-p > 2.

It follows that (d-1)! == 1 (mod q), and so q divides A033312(d-1).

Listed terms correspond to d = 12, 30, 76 (cf. A286230). Further terms should have d>=140.

Also, primes p=prime(n) such that A275111(n)=1, and (prime(n),prime(n+1)) are not twin primes (i.e., p is not a term of A001359).

LINKS

Table of n, a(n) for n=1..3.

EXAMPLE

For a(1)=7841, we have 7841! == 1 (mod 7853), where 7841 and 7853=7841+12 are consecutive primes. Also, 7853 | (12-1)!-1.

CROSSREFS

Cf. A275111, A286208.

Sequence in context: A250026 A194352 A234477 * A045277 A099498 A286208

Adjacent sequences:  A286178 A286179 A286180 * A286182 A286183 A286184

KEYWORD

bref,nonn,more

AUTHOR

Max Alekseyev and Thomas Ordowski, May 04 2017

STATUS

approved

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Last modified May 13 08:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)