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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 Table of n, a(n) for n=1..4. CROSSREFS Cf. A275111, A286181, A286208. Sequence in context: A259127 A296257 A301774 * A083175 A019258 A124903 Adjacent sequences: A286227 A286228 A286229 * A286231 A286232 A286233 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.)