

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.


3



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
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OFFSET

0,1


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


REFERENCES

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


LINKS



EXAMPLE

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



