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Search: id:A084165
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| A084165 |
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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. |
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+0
4
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| 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
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1,1
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COMMENT
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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.
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REFERENCES
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Handbook of First Complex Prime Numbers, Part1+2 Ervand Kogbetliantz and Alice Krikorian, Gordon and Breach, 1971
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EXAMPLE
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89 is the 11th prime in sequence A002313, 11*8 = 88, so 89 = 1 mod 11
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CROSSREFS
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Cf. A002313, A084163, A084166.
Sequence in context: A123079 A038938 A053028 this_sequence A120130 A087484 A019382
Adjacent sequences: A084162 A084163 A084164 this_sequence A084166 A084167 A084168
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KEYWORD
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nonn
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AUTHOR
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Sven Simon (sven-h.simon(AT)t-online.de), May 17 2003
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