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Search: id:A152658
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| A152658 |
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Beginnings of maximal chains of primes. |
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14
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..10000
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EXAMPLE
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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.
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PROGRAM
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(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) ];
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CROSSREFS
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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).
Sequence in context: A060182 A147066 A133204 this_sequence A100877 A007521 A078598
Adjacent sequences: A152655 A152656 A152657 this_sequence A152659 A152660 A152661
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 10 2008
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