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A237495 Primes which start a Cunningham chain of length 5 where every prime in the chain is the smaller of a pair of twin primes. 1
41887255409, 364223689829, 376655795669, 790031896499, 1558600513469, 2180283962009, 3266149150109, 4424063189699, 4655123392919, 6924093600269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is subset of the sequence A236443. Of the first 10000 terms in the sequence A236443 only 48 have length 5.

a(n) generates a Cunningham chain of length 5 and a_n(i) + 2 is also prime for i = 1,2,3,4 and 5.

This sequence is infinite under Dickson's conjecture.

LINKS

Abhiram R Devesh, Table of n, a(n) for n = 1..48

Chris Caldwell,Cunningham Chain

EXAMPLE

a(1) = 41887255409, with associated Cunningham chain of length 5: 41887255409, 83774510819, 167549021639, 335098043279, 670196086559, each of which is the smaller 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)

CROSSREFS

Cf. A178421, A005602, A236443 is a superset of this sequence.

Sequence in context: A172631 A172721 A259350 * A227387 A179227 A003940

Adjacent sequences:  A237492 A237493 A237494 * A237496 A237497 A237498

KEYWORD

nonn,hard,more

AUTHOR

Abhiram R Devesh, Feb 08 2014

STATUS

approved

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Last modified June 30 09:38 EDT 2022. Contains 354920 sequences. (Running on oeis4.)