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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

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Last modified April 10 22:25 EDT 2021. Contains 342856 sequences. (Running on oeis4.)