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).

359, 1069199, 1392269, 2614169, 10528649, 16981379, 18287309, 19463519, 21071489, 21171509, 22121579, 24857639, 40887569, 41809259, 76130129, 88362479, 118136279, 128893049, 131612609, 153318449, 289743689, 315495539

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)
# Program doesn't compile: pf not defined. Also, the while loop condition is immediately false. Robert C. Lyons, Nov 24 2024
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: A344284 A179678 A101996 * A360943 A097570 A185641

Adjacent sequences: A237014 A237015 A237016 * A237018 A237019 A237020

Keyword

nonn

Author

Abhiram R Devesh, Feb 02 2014

Status

approved