

A152658


Beginnings of maximal chains of primes.


14



5, 13, 29, 37, 43, 61, 89, 109, 131, 139, 227, 251, 269, 277, 293, 359, 389, 401, 449, 461, 491, 547, 569, 607, 631, 743, 757, 773, 809, 857, 887, 947, 971, 991, 1069, 1109, 1151, 1163, 1187, 1237, 1289, 1301, 1319, 1373, 1427, 1453, 1481, 1499, 1549, 1601
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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+r1. A chain of primes prime(k), ..., prime(k+r) is maximal if it is not part of a longer chain, i.e. if neither (k1)*prime(k1) + 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((n1)*PreviousPrime(p) +n*p) ) and IsPrime((n)*p+(n+1)*NextPrime(p)) where p is NthPrime(n) ];


CROSSREFS

Cf. A152117 (n*(nth prime) + (n+1)*((n+1)th prime)), A152657 (secluded primes), A119487 (primes of the form i*(ith prime) + (i+1)*((i+1)th prime), linking primes).
Cf. A105454  Zak Seidov, Feb 04 2016
Sequence in context: A207040 A309588 A268614 * A100877 A261580 A007521
Adjacent sequences: A152655 A152656 A152657 * A152659 A152660 A152661


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Dec 10 2008


STATUS

approved



