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Search: id:A084163
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| A084163 |
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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 A084164 Primes which are 1 mod m can be found in sequence A084165. |
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+0
4
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| 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; listen)
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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. 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.
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EXAMPLE
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197 is the 22th prime in sequence A002313, 22*9 = 198, so 197 = -1 mod 22
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CROSSREFS
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Cf. A002313, A084164, A084165.
Adjacent sequences: A084160 A084161 A084162 this_sequence A084164 A084165 A084166
Sequence in context: A106075 A137226 A106019 this_sequence A086149 A066502 A125870
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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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