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.

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

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 1-2.

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