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 A237017 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of the prime number pair (p, p+8). 0
 359, 1069199, 1392269, 2614169, 10528649, 16981379, 18287309, 19463519, 21071489, 21171509, 22121579, 24857639, 40887569, 41809259, 76130129, 88362479, 118136279, 128893049, 131612609, 153318449, 289743689, 315495539 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) generates a Cunningham chain of length 4 and a_n(i) + 8 is also prime for i = 1,2,3 and 4. This sequence is infinite under Dickson's conjecture. LINKS Table of n, a(n) for n=1..22. Chris K. Caldwell, Cunningham chain EXAMPLE a(1)=359, with associated Cunningham chain 359, 719, 1439, 2879; all of which are the lower member of a pair (p, p+8). (359,367) (719,727) (1439,1447) (2879,2887) PROG (Python) p1=2 n=4 mx=10 count=0 while p1>2: ....## Generate the a chain of numbers with length 4 ....cc=[] ....cc.append(p1) ....for i in range(1, n): ........cc.append((2**(i)*p1+((2**i)-1))) ....## chain entries + 8 ....cc2=[c+8 for c in cc] ....## check if cc is a Cunningham Chain ....## pf.isp_list returns True or false for a given list of numbers ....## if they are prime or not ....## ....pcc=pf.isp_list(cc) ....pcc2=pf.isp_list(cc2) ....## Number of primes for cc ....npcc=pcc.count(True) ....## Number of primes for cc2 ....npcc2=pcc2.count(True) ....if npcc==n and npcc2==n: ........print "For length ", n, " the series is : ", cc, " and ", cc2 ....p1=pf.nextp(p1) CROSSREFS Cf. A236443, A178421, A005602, A059763 Sequence in context: A344284 A179678 A101996 * A360943 A097570 A185641 Adjacent sequences: A237014 A237015 A237016 * A237018 A237019 A237020 KEYWORD nonn AUTHOR Abhiram R Devesh, Feb 02 2014 STATUS approved

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Last modified August 8 04:35 EDT 2024. Contains 375018 sequences. (Running on oeis4.)