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A060255
Smaller of twin primes {p, p+2} whose average p+1 = k*q is the least multiple of the n-th primorial number q such that k*q-1 and k*q+1 are twin primes.
1
3, 5, 29, 419, 2309, 180179, 4084079, 106696589, 892371479, 103515091679, 4412330782859, 29682952539239, 22514519501013539, 313986271960080719, 22750921955774182169, 912496437361321252439, 26918644902158976946979
OFFSET
1,1
FORMULA
a(n) = p = k(n)*q(n)-1, where q(n)=A002110(n) and k(n)=A060256(n) is the smallest integer whose multiplication by the n-th primorial yields p+1.
EXAMPLE
a(13) = -1 + (2*3*5*7*...*41)*k(13) = 304250263527210*74 and {22514519501013539, 22514519501013542} are the corresponding primes; k(13)=74 is the smallest suitable multiplier. Twin primes obtained from primorial numbers with k=1 multiplier seem to be much rarer (see A057706).
For j=1,2,3,4,5,6, a(j)=A001359(1), A059960(1), A060229(1), A060230(1), A060231(1), A060232(1) respectively.
PROG
(PARI) a(n) = {my(q = prod(k=1, n, prime(k))); for(k=1, oo, if (isprime(q*k-1) && isprime(q*k+1), return(q*k-1)); ); } \\ Michel Marcus, Jul 10 2018
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 22 2001
EXTENSIONS
a(2)=5 corrected by Ray Chandler, Apr 03 2009
STATUS
approved