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A236443 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of twin prime. 3
253679, 1138829, 58680929, 90895769, 124253009, 269877299, 392071679, 613813199, 1014342209, 1277981669, 1413015029, 1453978679, 1753585679, 2919331379, 3424037189, 3538972709, 4025789039, 4175762009, 4362439199, 4843208789, 5708418869, 5795508599 (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) + 2 is also prime for i = 1,2,3 and 4.

This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Jan 29 2014

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Chris Caldwell, Cunningham chain

EXAMPLE

a(1)=253679, with associated Cunningham chain 253679, 507359, 1014719, 2029439, all of which are the lower member of a pair of twin primes.

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 + 2

....cc2=[c+2 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)

(PARI) is(n)=n%210==209 && isprime(n) && isprime(n+2) && isprime(2*n+1) && isprime(2*n+3) && isprime(4*n+3) && isprime(4*n+5) && isprime(8*n+7) && isprime(8*n+9)

forstep(n=419, 1e9, [1470, 420, 420], if(is(n), print(n))) \\ Charles R Greathouse IV, Jan 29 2014

CROSSREFS

Cf. A178421, A005602, A059763.

Sequence in context: A236874 A236163 A140967 * A069176 A253725 A140079

Adjacent sequences:  A236440 A236441 A236442 * A236444 A236445 A236446

KEYWORD

nonn

AUTHOR

Abhiram R Devesh, Jan 26 2014

EXTENSIONS

More terms from T. D. Noe, Jan 29 2014

STATUS

approved

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Last modified July 12 05:35 EDT 2020. Contains 335658 sequences. (Running on oeis4.)