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

0,1

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

Table of n, a(n) for n=0..37.

Example

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

Crossrefs

Cf. A002313, A084161.

Sequence in context: A369587 A366719 A129733 * A238139 A268722 A213828

Adjacent sequences: A084157 A084158 A084159 * A084161 A084162 A084163

Keyword

nonn

Author

Sven Simon, May 17 2003

Status

approved