login
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
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
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, Jan 26 2014
EXTENSIONS
More terms from T. D. Noe, Jan 29 2014
STATUS
approved