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A237495
Primes which start a Cunningham chain of length 5 where every prime in the chain is the smaller of a pair of twin primes.
1
41887255409, 364223689829, 376655795669, 790031896499, 1558600513469, 2180283962009, 3266149150109, 4424063189699, 4655123392919, 6924093600269
OFFSET
1,1
COMMENTS
This is subset of the sequence A236443. Of the first 10000 terms in the sequence A236443 only 48 have length 5.
a(n) generates a Cunningham chain of length 5 and a_n(i) + 2 is also prime for i = 1,2,3,4 and 5.
This sequence is infinite under Dickson's conjecture.
LINKS
Chris Caldwell,Cunningham Chain
EXAMPLE
a(1) = 41887255409, with associated Cunningham chain of length 5: 41887255409, 83774510819, 167549021639, 335098043279, 670196086559, each of which is the smaller of a pair of twin primes.
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 + 2
....cc2=[c+2 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. A178421, A005602, A236443 is a superset of this sequence.
Sequence in context: A172631 A172721 A259350 * A227387 A179227 A003940
KEYWORD
nonn,hard,more
AUTHOR
Abhiram R Devesh, Feb 08 2014
STATUS
approved