login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 17:17 EDT 2022. Contains 356945 sequences. (Running on oeis4.)