A084160 First occurrence prime gaps of the primes in sequence A002313 (Real primes with corresponding complex primes). a(0) = 2 with length of gap 3. For n>0 the size of the gap in the sequence is 4n, a(n) is the starting prime of the gap.

2, 13, 5, 17, 73, 293, 113, 1153, 197, 2557, 1321, 1553, 461, 2161, 1493, 1801, 10993, 9533, 15661, 27817, 76001, 24593, 16741, 40709, 53453, 58789, 62297, 33181, 256189, 110321, 112757, 344497, 39581, 138661, 269761, 448421, 78989, 50593

Offset: 0

Author

Sven Simon, May 17 2003

Keywords

• nonn

Comments

Real primes 2,5,13,17,29,37,... have a unique representation as sum of two squares. Values larger 2 are the primes p with p = 1 mod 4. This is sequence A002313. If p = x^2 + y^2, the corresponding complex prime is x+y*i

Examples

			a(3) = 17 because the next prime in sequence A002313 is 29, the size of the gap is 3*4 = 12.
		

References

• Handbook of First Complex Prime Numbers, Part1+2 Ervand Kogbetliantz and Alice Krikorian, Gordon and Breach, 1971

Crossrefs

Cf. A002313, A084161.