

A152657


Secluded primes.


3



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
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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+r1.


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((n1)*NthPrime(n1)+k)) and not IsPrime(k+(n+1)*NthPrime(n+1)) where k is n*p where p is NthPrime(n) ];


CROSSREFS

Cf. A152117 (n*(nth prime) + (n+1)*((n+1)th prime)), A152658 (beginnings of maximal chains of primes), A119487 (primes of the form i*(ith prime) + (i+1)*((i+1)th prime), linking primes).
Sequence in context: A054313 A080052 A157190 * A299172 A154253 A097961
Adjacent sequences: A152654 A152655 A152656 * A152658 A152659 A152660


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Dec 10 2008


STATUS

approved



