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%I #15 May 17 2021 15:03:11
%S 8629739,77115359,173508869,343621919,419597309,573556349,763154039,
%T 770676239,847344419,851521949,951418229,1014432869,1252780829,
%U 1260053939,1322933519,1529921909,1569236309,1861760819,1954231199,2048205689,2071334939,2583377789,2658083819
%N Smaller member of a Sophie Germain pair in which each member of the pair is the smallest of its prime triple (p, (p^3)+2, (p^5)+2).
%H Abhiram R Devesh, <a href="/A242346/b242346.txt">Table of n, a(n) for n = 1..40</a>
%e a(1): p = 8629739; (2*p)+1 = 17259479
%e Prime Triplets of the form (p,(p^3)+2,(p^5)+2): (8629739, 642677333350934910421, 47861720360612147562343307996312701 );(17259479, 5141419560476273559241, 1531575495230651978949727458917513401)
%o (Python)
%o p1=2
%o n=2
%o count=0
%o while p1>2:
%o ....## Generate the pair
%o ....cc=[]
%o ....cc.append(p1)
%o ....for i in range(1, n):
%o ........cc.append((2**(i)*p1+((2**i)-1)))
%o ....## chain entries cubed + 2
%o ....cc2=[(c*c*c)+2 for c in cc]
%o ....## chain entries power to 5 + 2
%o ....cc3=[(c**5)+2 for c in cc]
%o ....## check if cc is a Sophie Germain Pair or not
%o ....## pf.isp_list returns True or false for a given list of numbers
%o ....## if they are prime or not
%o ....##
%o ....pcc=pf.isp_list(cc)
%o ....pcc2=pf.isp_list(cc2)
%o ....pcc3=pf.isp_list(cc3)
%o ....## Number of primes for cc, cc2, cc3
%o ....npcc=pcc.count(True)
%o ....npcc2=pcc2.count(True)
%o ....npcc3=pcc3.count(True)
%o ....if npcc==n and npcc2==n and npcc3==n:
%o ........print "For length ", n, " the series is : ", cc, ",", cc2 ," and ", cc3
%o ....p1=pf.nextp(p1)
%Y Cf. A048636, A237188, A237256.
%K nonn,hard
%O 1,1
%A _Abhiram R Devesh_, May 11 2014
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