

A084165


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 A084166 Primes which are 1 mod m can be found in sequence A084163.


3



5, 13, 17, 37, 89, 97, 181, 2689, 2969, 4621, 7457, 8081, 8161, 36709, 62701, 169489, 169709, 169753, 282809, 770101, 5763577, 9491101, 9491281, 9495121, 42544261, 115195501, 189689041, 189689653, 312315373, 312316409, 2294883817
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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


LINKS

Table of n, a(n) for n=1..31.


EXAMPLE

89 is the 11th prime in sequence A002313, 11*8 = 88, so 89 = 1 mod 11


MATHEMATICA

Module[{nn=112*10^6, pr, len}, pr=Select[Prime[Range[nn]], MemberQ[ {1, 2}, Mod[ #, 4]]&]; len=Length[pr]; Select[Thread[{pr, Range[len]}], Mod[ #[[1]], #[[2]]] == 1&]][[All, 1]] (* Harvey P. Dale, Aug 13 2020 *)


CROSSREFS

Cf. A002313, A084163, A084166.
Sequence in context: A248980 A188131 A172459 * A120130 A087484 A019382
Adjacent sequences: A084162 A084163 A084164 * A084166 A084167 A084168


KEYWORD

nonn


AUTHOR

Sven Simon, May 17 2003


STATUS

approved



