OFFSET
1,1
COMMENTS
A sequence of consecutive primes prime(k), ..., prime(k+r), r >= 1, is called a chain of primes if i*prime(i) + (i+1)*prime(i+1) is prime (the linking prime for prime(i) and prime(i+1), cf. A119487) for i from k to k+r-1. A chain of primes prime(k), ..., prime(k+r) is maximal if it is not part of a longer chain, i.e. if neither (k-1)*prime(k-1) + k*prime(k) nor (k+r)*prime(k+r) + (k+r+1)*prime(k+r+1) is prime.
A chain of primes has two or more members; a prime is called secluded if it is not member of a chain of primes (cf. A152657).
LINKS
Klaus Brockhaus, Table of n, a(n) for n=1..10000
EXAMPLE
3*prime(3) + 4*prime(4) = 3*5 + 4*7 = 43 is prime and 4*prime(4) + 5*prime(5) = 4*7 + 5*11 = 83 is prime, so 5, 7, 11 is a chain of primes. 2*prime(2) + 3*prime(3) = 2*3 + 3*5 = 21 is not prime and 5*prime(5) + 6*prime(6) = 5*11 + 6*13 = 133 is not prime, hence 5, 7, 11 is maximal and prime(3) = 5 is the beginning of a maximal chain.
PROG
(Magma) [ p: n in [1..253] | (n eq 1 or not IsPrime((n-1)*PreviousPrime(p) +n*p) ) and IsPrime((n)*p+(n+1)*NextPrime(p)) where p is NthPrime(n) ];
CROSSREFS
Cf. A152117 (n*(n-th prime) + (n+1)*((n+1)-th prime)), A152657 (secluded primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes).
Cf. A105454 - Zak Seidov, Feb 04 2016
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Dec 10 2008
STATUS
approved