A242281 - OEIS

%I #15 May 15 2014 10:58:11

%S 419,761,911,1601,2351,6269,6551,9029,22259,28559,28949,37139,52571,

%T 56531,67559,70379,78509,108359,114641,133571,135119,138179,146669,

%U 153449,176021,187409,193841,200639,252761,288731,303581,312551,333479,337349,407639,408389

%N Smaller member of a Sophie Germain pair in which each member of the pair is the smaller of its prime pair (p, (p*p*p)+2).

%H Abhiram R Devesh, <a href="/A242281/b242281.txt">Table of n, a(n) for n = 1..675</a>

%e a(1): p = 419; (2*p)+1 = 839

%e Prime Pairs of the form (p,p**3+2): (419, 73560061) and (839, 590589721)

%e a(2): p = 761; (2*p)+1 = 1523

%e Prime Pairs (761, 440711083) and (1523, 3532642669)

%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 ....## 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 ....## Number of primes for cc

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

%o ....## Number of primes for cc2

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

%o ....if npcc==n and npcc2==n:

%o ........print "For length ", n, " the series is : ", cc, " and ", cc2

%o ....p1=pf.nextp(p1)

%Y Cf. A048636, A237188, A237256.

%K nonn,hard

%O 1,1

%A _Abhiram R Devesh_, May 10 2014