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Search: id:A131462
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| A131462 |
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Residues of 3^(2^p(n)-1) for Mersenne numbers with prime indices. |
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+0
6
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| 0, 3, 3, 3, 992, 3, 3, 3, 877681, 195496587, 3, 36787319437, 1423919640546, 3542630063906, 77319946053101, 6458069995222223, 168313041233693968, 3, 139200566017647400916, 207875641949796659481
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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M_p is prime iff 3 ^ M_p is congruent to 3 mod M_p. Thus M_7 = 127 is prime because 3^127 mod 127 = 3 while M_11 = 2047 is composite because 3^2047 mod 2047 <> 3.
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LINKS
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Dennis Martin, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = 3^(2^p(n)-1) mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^11-1) mod 2^11-1 = 3^2047 mod 2047 = 992
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CROSSREFS
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Cf. A095847, A001348, A131458, A131459, A131460, A131461, A131463.
Sequence in context: A091323 A118539 A015665 this_sequence A117032 A078911 A082899
Adjacent sequences: A131459 A131460 A131461 this_sequence A131463 A131464 A131465
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KEYWORD
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nonn
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AUTHOR
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Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 20 2007
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