A094249 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,...

53, 353, 433, 733, 1609, 7789

Offset: 0

Author

Sven Simon, Apr 25 2004

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Cf. A002313.