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A237256 Smallest member of Sophie Germain pair, wherein each member of the prime pair is the smallest of its prime quadruplets (p, p+2, p+8, p+12). 3
5, 29, 41609, 4287599, 16254449, 87130709, 118916729, 157119089, 173797289, 180210059, 207959879, 309740999, 349066439, 356259989, 401519399, 473953229, 705480749, 912950249, 994719629 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is not known if there are infinitely many Sophie Germain pairs with this property.

LINKS

Abhiram R Devesh and Dana Jacobsen, Table of n, a(n) for n = 1..1155 [first 155 terms from Abhiram R Devesh]

Eric Weisstein's World of Mathematics, Sophie Germain Prime

Wikipedia, Sophie Germain Prime

EXAMPLE

a(1): p = 5; (2*p)+1 = 11; prime quadruplets (5,7,13,17); (11,13,19,23).

a(2): p = 29; (2*p)+1 = 59; prime quadruplets (29,31,37,41); (59,61,67,71).

PROG

(Python)

p1=2

n=2

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]

....## chain entries + 8

....cc8=[c+8 for c in cc]

....## chain entries + 12

....cc12=[c+12 for c in cc]

....## check if cc is a Sophie Germain Pair or not

....## 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)

....pcc8=pf.isp_list(cc8)

....pcc12=pf.isp_list(cc12) ....## Number of primes for cc

....npcc=pcc.count(True)

....## Number of primes for cc2

....npcc2=pcc2.count(True)

....## Number of primes for cc8

....npcc8=pcc8.count(True)

....## Number of primes for cc12

....npcc12=pcc12.count(True)

....if npcc==n and npcc2==n and npcc8==n and npcc12==n:

........print "For length ", n, " the series is : ", cc, " , ", cc2, " , ", cc8, " and " cc12

....p1=pf.nextp(p1)

(PARI) forprime(p=1, 1e9, my(t=2*p+1); if(isprime(t) && isprime(p+2) && isprime(p+8) && isprime(p+12) && isprime(t+2) && isprime(t+8) && isprime(t+12), print1(p, ", "))) \\ Felix Fröhlich, Jul 26 2014

(Perl) use ntheory ":all"; my @p = sieve_prime_cluster(1, 2e9, 2, 8, 12); my %h; undef @h{@p}; for (@p) { say if exists $h{2*$_+1} } # Dana Jacobsen, Oct 03 2015

CROSSREFS

Cf. A005384, A233540.

Sequence in context: A086720 A056869 A228028 * A172041 A187605 A266569

Adjacent sequences:  A237253 A237254 A237255 * A237257 A237258 A237259

KEYWORD

nonn

AUTHOR

Abhiram R Devesh, Feb 05 2014

STATUS

approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)