

A237017


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).


0



359, 1069199, 1392269, 2614169, 10528649, 16981379, 18287309, 19463519, 21071489, 21171509, 22121579, 24857639, 40887569, 41809259, 76130129, 88362479, 118136279, 128893049, 131612609, 153318449, 289743689, 315495539
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Table of n, a(n) for n=1..22.
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

Cf. A236443, A178421, A005602, A059763
Sequence in context: A013325 A179678 A101996 * A097570 A185641 A031966
Adjacent sequences: A237014 A237015 A237016 * A237018 A237019 A237020


KEYWORD

nonn


AUTHOR

Abhiram R Devesh, Feb 02 2014


STATUS

approved



