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A286230 Possible differences between consecutive primes p, q satisfying p! == 1 (mod q). 3
2, 12, 30, 76 (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, so 2 is a term.
Terms d > 2 correspond to Wilson's pseudo-twin primes, i.e., consecutive primes p, q such that q - p = d and p! == 1 (mod q). The corresponding primes are listed in A286181 and A286208.
As a set, the sequence is the union of {2} and the differences {A286208(n) - A286181(n)}.
A positive integer d belongs to this sequence if A033312(d-1) = (d-1)! - 1 has a prime factor q such that q - A151799(q) = d.
All terms are even.
If it exists, a(5) >= 140.
LINKS
CROSSREFS
Sequence in context: A259127 A296257 A301774 * A083175 A019258 A124903
KEYWORD
bref,nonn,more
AUTHOR
Max Alekseyev, May 04 2017
STATUS
approved

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Last modified June 22 08:18 EDT 2024. Contains 373567 sequences. (Running on oeis4.)