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
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
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, Feb 02 2014
STATUS
approved