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

1,1

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.

Links

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

Example

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.

Prog

(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) ];

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).

Sequence in context: A080052 A376675 A157190 * A299172 A154253 A097961

Adjacent sequences: A152654 A152655 A152656 * A152658 A152659 A152660

Keyword

nonn

Author

Klaus Brockhaus, Dec 10 2008

Status

approved