A152657 Secluded primes.

2, 3, 59, 83, 107, 127, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 239, 241, 263, 311, 313, 317, 331, 337, 347, 349, 353, 373, 379, 383, 419, 421, 431, 433, 439, 443, 467, 479, 487, 503, 509, 521, 523, 541, 563, 577, 587, 593, 599, 601, 617

Offset: 1

Author

Klaus Brockhaus, Dec 10 2008

Keywords

• nonn

Comments

A prime p is called secluded if it is not member of a chain of primes. 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 for i from k to k+r-1.

Examples

			16*prime(16) + 17*prime(17) = 16*53 + 17*69 = 1851 = 3*617 is not prime; 17*prime(17) + 18*prime(18) = 17*59 + 18*61 = 2101 = 11+191 is not prime. Hence prime(17) = 59 is secluded.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A152117 (n*(n-th prime) + (n+1)*((n+1)-th prime)), A152658 (beginnings of maximal chains of primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes).

Programs

Magma

[ p: n in [1..113] | (n eq 1 or not IsPrime((n-1)*NthPrime(n-1)+k)) and not IsPrime(k+(n+1)*NthPrime(n+1)) where k is n*p where p is NthPrime(n) ];