

A084163


Primes which are 1 mod m, where m is the index of the prime in sequence A002313 (Real primes with corresponding complex primes). The index m can be found in A084164 Primes which are 1 mod m can be found in sequence A084165.


3



29, 41, 197, 229, 269, 2617, 2729, 2897, 4649, 37201, 37277, 169553, 170081, 170873, 282577, 9491309, 9493889, 15614761, 69955373, 69955577, 115195429, 115196129, 312316481, 513773717, 846651233, 3778288373, 3778289381, 3778290641
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OFFSET

1,1


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. First complex prime is 1+i with 2 as corresponding real prime, according to reference, page 12.


REFERENCES

Handbook of First Complex Prime Numbers, Part1+2 Ervand Kogbetliantz and Alice Krikorian, Gordon and Breach, 1971. The list in Part 2 contains an error: on page 919, column 2, number 5 is printed twice, so the indices after that number are wrong.


LINKS

Table of n, a(n) for n=1..28.


EXAMPLE

197 is the 22nd prime in sequence A002313, 22*9 = 198, so 197 = 1 mod 22.


CROSSREFS

Cf. A002313, A084164, A084165.
Sequence in context: A106075 A238666 A106019 * A181622 A355599 A086149
Adjacent sequences: A084160 A084161 A084162 * A084164 A084165 A084166


KEYWORD

nonn


AUTHOR

Sven Simon, May 17 2003


STATUS

approved



