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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A369587 A366719 A129733 * A238139 A268722 A213828
KEYWORD
nonn
AUTHOR
Sven Simon, May 17 2003
STATUS
approved

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Last modified June 17 15:17 EDT 2024. Contains 373450 sequences. (Running on oeis4.)