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Search: id:A131463
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| A131463 |
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Residues of 3^(2^p(n)) for Mersenne numbers with prime indices. |
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+0
6
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| 0, 2, 9, 9, 929, 9, 9, 9, 2633043, 49618850, 9, 110361958311, 2072735666087, 1831797169511, 91222349803976, 1359811476184687, 504939123701081904, 9, 122453792873589376894, 623626925849389978443
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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+1) is congruent to 9 mod M_p. Thus M_7 = 127 is prime because 3^128 mod 127 = 9 while M_11 = 2047 is composite because 3^2048 mod 2047 <> 9.
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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)) mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^11) mod 2^11-1 = 3^2048 mod 2047 = 929
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CROSSREFS
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Cf. A095847, A001348, A131458, A131459, A131460, A131461, A131462.
Sequence in context: A109322 A000587 A014182 this_sequence A065644 A043065 A077214
Adjacent sequences: A131460 A131461 A131462 this_sequence A131464 A131465 A131466
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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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