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%I #23 Apr 03 2023 10:36:13
%S 253679,1138829,58680929,90895769,124253009,269877299,392071679,
%T 613813199,1014342209,1277981669,1413015029,1453978679,1753585679,
%U 2919331379,3424037189,3538972709,4025789039,4175762009,4362439199,4843208789,5708418869,5795508599
%N Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of twin prime.
%C a(n) generates a Cunningham chain of length 4 and a_n(i) + 2 is also prime for i = 1,2,3 and 4.
%C This sequence is infinite under Dickson's conjecture. - _Charles R Greathouse IV_, Jan 29 2014
%H Charles R Greathouse IV, <a href="/A236443/b236443.txt">Table of n, a(n) for n = 1..10000</a>
%H Chris Caldwell, <a href="https://t5k.org/glossary/xpage/CunninghamChain.html">Cunningham chain</a>
%e a(1)=253679, with associated Cunningham chain 253679, 507359, 1014719, 2029439, all of which are the lower member of a pair of twin primes.
%o (Python)
%o p1=2
%o n=4
%o mx=10
%o count=0
%o while p1>2:
%o ....## Generate the a chain of numbers with length 4
%o ....cc=[]
%o ....cc.append(p1)
%o ....for i in range(1,n):
%o ........cc.append((2**(i)*p1+((2**i)-1)))
%o ....## chain entries + 2
%o ....cc2=[c+2 for c in cc]
%o ....## check if cc is a Cunningham Chain
%o ....## pf.isp_list returns True or false for a given list of numbers
%o ....## if they are prime or not
%o ....##
%o ....pcc=pf.isp_list(cc)
%o ....pcc2=pf.isp_list(cc2)
%o ....## Number of primes for cc
%o ....npcc=pcc.count(True)
%o ....## Number of primes for cc2
%o ....npcc2=pcc2.count(True)
%o ....if npcc==n and npcc2==n:
%o ........print "For length ",n," the series is : ",cc," and ",cc2
%o ....p1=pf.nextp(p1)
%o (PARI) is(n)=n%210==209 && isprime(n) && isprime(n+2) && isprime(2*n+1) && isprime(2*n+3) && isprime(4*n+3) && isprime(4*n+5) && isprime(8*n+7) && isprime(8*n+9)
%o forstep(n=419,1e9,[1470, 420, 420],if(is(n),print(n))) \\ _Charles R Greathouse IV_, Jan 29 2014
%Y Cf. A178421, A005602, A059763.
%K nonn
%O 1,1
%A _Abhiram R Devesh_, Jan 26 2014
%E More terms from _T. D. Noe_, Jan 29 2014
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