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Search: id:A131458
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| A131458 |
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Residues of 3^(2^(p(n)-1)-1) for Mersenne numbers with prime indices. |
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+0
6
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| 0, 6, 30, 126, 1565, 8190, 131070, 524286, 7511964, 89777599, 2147483646, 20166585982, 840455563322, 4787976306682, 5519162753736, 2617809209727498, 334169564069012755, 2305843009213693950, 47306781863857413639
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Mp is prime iff 3^(2^(p(n)-1)-1) is congruent to (-1) Mod Mp. Thus M7 = 127 is prime because 3^63 Mod 127 = 126 (=127-1) while M11 = 2047 is composite because 3^1023 Mod 2047 <> 2046.
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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)-1) Mod 2^p(n)-1
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EXAMPLE
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a(5) = 3^(2^(11-1)-1) Mod 2^11-1 = 3^1023 Mod 2047 = 1565
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CROSSREFS
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Cf. A095847, A001348, A131459, A131460, A131461, A131462, A131463.
Adjacent sequences: A131455 A131456 A131457 this_sequence A131459 A131460 A131461
Sequence in context: A074009 A002446 A002934 this_sequence A032205 A007465 A073389
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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 13 2007, Jul 20 2007
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