A047976 Let (p1,p2), (p3,p4) be pairs of twin primes with p1*p2=p3+p4-1; sequence gives values of p1.

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

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