%I #9 Apr 03 2023 10:36:13
%S 359,1069199,1392269,2614169,10528649,16981379,18287309,19463519,
%T 21071489,21171509,22121579,24857639,40887569,41809259,76130129,
%U 88362479,118136279,128893049,131612609,153318449,289743689,315495539
%N 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).
%C a(n) generates a Cunningham chain of length 4 and a_n(i) + 8 is also prime for i = 1,2,3 and 4.
%C This sequence is infinite under Dickson's conjecture.
%H Chris K. Caldwell, <a href="https://t5k.org/glossary/xpage/CunninghamChain.html">Cunningham chain</a>
%e a(1)=359, with associated Cunningham chain 359, 719, 1439, 2879; all of which are the lower member of a pair (p, p+8).
%e (359,367)
%e (719,727)
%e (1439,1447)
%e (2879,2887)
%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 + 8
%o ....cc2=[c+8 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)
%Y Cf. A236443, A178421, A005602, A059763
%K nonn
%O 1,1
%A _Abhiram R Devesh_, Feb 02 2014