%I #17 Apr 03 2023 10:36:13
%S 41887255409,364223689829,376655795669,790031896499,1558600513469,
%T 2180283962009,3266149150109,4424063189699,4655123392919,6924093600269
%N Primes which start a Cunningham chain of length 5 where every prime in the chain is the smaller of a pair of twin primes.
%C This is subset of the sequence A236443. Of the first 10000 terms in the sequence A236443 only 48 have length 5.
%C 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.
%C This sequence is infinite under Dickson's conjecture.
%H Abhiram R Devesh, <a href="/A237495/b237495.txt">Table of n, a(n) for n = 1..48</a>
%H Chris Caldwell,<a href="https://t5k.org/glossary/xpage/CunninghamChain.html">Cunningham Chain</a>
%e 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.
%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)
%Y Cf. A178421, A005602, A236443 is a superset of this sequence.
%K nonn,hard,more
%O 1,1
%A _Abhiram R Devesh_, Feb 08 2014