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Sequence A002313 is the sequence of primes p = a*a + b*b, starting 2,5,13,17,..., members p > 2 have p = 1 mod 4. In analogy to the definition of primorial primes use the primes of sequence A002313 to build the product, written here as cp#353+1 or cp#1609-1. If cp#n+1 or cp#n-1 is prime, then n is in the sequence. Using +1 or -1 to define the type of prime cp#n+-1 we get the sequence 1,1,1,1,-1,1,...
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%I #3 Mar 31 2012 10:28:43

%S 53,353,433,733,1609,7789

%N Sequence A002313 is the sequence of primes p = a*a + b*b, starting 2,5,13,17,..., members p > 2 have p = 1 mod 4. In analogy to the definition of primorial primes use the primes of sequence A002313 to build the product, written here as cp#353+1 or cp#1609-1. If cp#n+1 or cp#n-1 is prime, then n is in the sequence. Using +1 or -1 to define the type of prime cp#n+-1 we get the sequence 1,1,1,1,-1,1,...

%C Primes of type cp#n-1 are in sequence A002313 again, only one such prime was found, cp#1609-1 was certified with Primo. 1609 = 40*40 + 3*3 = 1600 + 9. Because of the starting value 2, cp#n+1 = 3 mod 4 for every possible n, so they are primes, but not primes of sequence A002313. The search limits were 32000 for primes cp#n+1 and 64000 for primes cp#n-1, having more than 10000 decimal digits in the range of 64000.

%e a(0) = 53 with cp#53+1 = 2*5*13*17*29*37*41*53 + 1 = 5152900091

%Y Cf. A002313.

%K nonn

%O 0,1

%A _Sven Simon_, Apr 25 2004