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 A047976 Let (p1,p2), (p3,p4) be pairs of twin primes with p1*p2=p3+p4-1; sequence gives values of p1. 4
 5, 11, 41, 71, 599, 641, 881, 2129, 2381, 2687, 3557, 3581, 4547, 6131, 7547, 8009, 9041, 13397, 13931, 15971, 17597, 19139, 21491, 26249, 26261, 34511, 38669, 39227, 39341, 48311, 49739, 52541, 53087, 53591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is also the lesser of two twin primes (p1,p2) given by: (p1+1)^2 = 2(p3+1) where (p3,p4) is also a twin prime pair with p4 = p3 + 2. There is at least one other value of h such that the more general equation (p1+1)^h = h*(p3+1) is true for two pairs of twin primes beyond the h=2 case: (p1,p2) = (29,31) satisfies the more general equation with h=8, corresponding to (p3,p4) = (82012499999, 82012500001). - Austin Hinkel, Dec 29 2022 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 5*7 = 17+19-1, so 5 is a term. 11*13 = 71+73-1, so 11 is a term. PROG (PARI) list(lim)=my(v=List(), p=3, r); forprime(q=5, lim+2, if(q-p==2 && isprime(r=p*q\2) && isprime(r+2), listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Sep 29 2015 (PARI) is(n)=isprime(n) && isprime(n+2) && isprime(n*(n+2)\2) && isprime(n*(n+2)\2+2) \\ Charles R Greathouse IV, Sep 29 2015 CROSSREFS Cf. A047977, A047978, A047979. Sequence in context: A023271 A159049 A343712 * A006382 A295504 A055113 Adjacent sequences: A047973 A047974 A047975 * A047977 A047978 A047979 KEYWORD nonn AUTHOR Naohiro Nomoto STATUS approved

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Last modified July 14 20:49 EDT 2024. Contains 374323 sequences. (Running on oeis4.)