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 A242346 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). 1
 8629739, 77115359, 173508869, 343621919, 419597309, 573556349, 763154039, 770676239, 847344419, 851521949, 951418229, 1014432869, 1252780829, 1260053939, 1322933519, 1529921909, 1569236309, 1861760819, 1954231199, 2048205689, 2071334939, 2583377789, 2658083819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Abhiram R Devesh, Table of n, a(n) for n = 1..40 EXAMPLE a(1): p = 8629739; (2*p)+1 = 17259479 Prime Triplets of the form (p,(p^3)+2,(p^5)+2): (8629739, 642677333350934910421, 47861720360612147562343307996312701 );(17259479, 5141419560476273559241, 1531575495230651978949727458917513401) 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] ....## chain entries power to 5 + 2 ....cc3=[(c**5)+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) ....pcc3=pf.isp_list(cc3) ....## Number of primes for cc, cc2, cc3 ....npcc=pcc.count(True) ....npcc2=pcc2.count(True) ....npcc3=pcc3.count(True) ....if npcc==n and npcc2==n and npcc3==n: ........print "For length ", n, " the series is : ", cc, ", ", cc2 , " and ", cc3 ....p1=pf.nextp(p1) CROSSREFS Cf. A048636, A237188, A237256. Sequence in context: A237074 A345616 A346333 * A015378 A337463 A151936 Adjacent sequences: A242343 A242344 A242345 * A242347 A242348 A242349 KEYWORD nonn,hard AUTHOR Abhiram R Devesh, May 11 2014 STATUS approved

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Last modified July 12 13:47 EDT 2024. Contains 374247 sequences. (Running on oeis4.)