A242281 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).

419, 761, 911, 1601, 2351, 6269, 6551, 9029, 22259, 28559, 28949, 37139, 52571, 56531, 67559, 70379, 78509, 108359, 114641, 133571, 135119, 138179, 146669, 153449, 176021, 187409, 193841, 200639, 252761, 288731, 303581, 312551, 333479, 337349, 407639, 408389

Offset

1,1

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..675

Example

a(1): p = 419; (2*p)+1 = 839
Prime Pairs of the form (p,p**3+2): (419, 73560061) and (839, 590589721)
a(2): p = 761; (2*p)+1 = 1523
Prime Pairs (761, 440711083) and (1523, 3532642669)

Prog

(Python)
p1=2
n=2
count=0
while p1>2:
....## Generate the pair
....cc=[]
....cc.append(p1)
....for i in range(1, n):
........cc.append((2**(i)*p1+((2**i)-1)))
....## chain entries cubed + 2
....cc2=[(c*c*c)+2 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)
....## 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. A048636, A237188, A237256.

Sequence in context: A097233 A233551 A142281 * A142733 A364359 A060230

Adjacent sequences: A242278 A242279 A242280 * A242282 A242283 A242284

Keyword

nonn,hard

Author

Abhiram R Devesh, May 10 2014

Status

approved