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Search: id:A097130
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| A097130 |
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Carmichael numbers that are not == 1 mod 24. |
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1
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| 561, 2465, 2821, 8911, 29341, 62745, 63973, 101101, 162401, 188461, 314821, 512461, 656601, 1024651, 1033669, 1152271, 1193221, 1909001, 2100901, 2508013, 2531845, 3146221, 5031181, 5444489, 5481451, 6733693, 6868261
(list; graph; listen)
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OFFSET
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561,1
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COMMENT
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91.18 % of all Carmichael numbers under 10^16 are 1 modulo 24. Only 4 are 3 modulo 24 and 858899288969751 is the only Carmichael number up to 10^16 that is 15 modulo 24. More terms available from the author.
Observe that testing p for primality with modulo 24 (p^2)-1 gives nearly identical results to Fermat's Little Theorem and even does not accept all Carmichaels as prime, eg: 8911: ((8911*8911)-1) modulo 24 is 11.
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REFERENCES
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Granville, Andrew and Pomerance, Carl, Two contradictory conjectures concerning Carmichael numbers. Math. Comp. 71 (2002),no. 238, 883-908.
Gorgui-Naguib and Dlay, Properties of the Euler totient function modulo 24 and some of its cryptographic implications, Cryptology Research Group, University of Newcastle-upon-Tyne, UK.
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LINKS
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F. Richman, Primality testing with Fermat's little theorem
See also: Gorgui-Naguib and Dlay Title?
Granville, Andrew and Pomerance, Carl, Two contradictory conjectures concerning Carmichael numbers
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FORMULA
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a(n) = if(mod(n, 24)<>1, n, 0)
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EXAMPLE
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561 leaves 9 modulo 24, 1105 leaves 1 modulo 24, 1729 leaves 1 modulo 24, etc.
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CROSSREFS
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Cf. A002997, A097061.
Sequence in context: A131672 A083732 A135720 this_sequence A110889 A063400 A141706
Adjacent sequences: A097127 A097128 A097129 this_sequence A097131 A097132 A097133
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KEYWORD
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nonn
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AUTHOR
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Rob Hoogers (chimera(AT)chimera.fol.nl), Jul 26 2004
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