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A124223
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Table T(n,k) = reciprocal of k modulo Prime(n), for 1 <= k < Prime(n).
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3
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1, 1, 2, 1, 3, 2, 4, 1, 4, 5, 2, 3, 6, 1, 6, 4, 3, 9, 2, 8, 7, 5, 10, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 1, 9, 6, 13, 7, 3, 5, 15, 2, 12, 14, 10, 4, 11, 8, 16, 1, 10, 13, 5, 4, 16, 11, 12, 17, 2, 7, 8, 3, 15, 14, 6, 9, 18, 1, 12, 8, 6, 14, 4, 10, 3, 18, 7, 21, 2, 16, 5, 20, 13, 19, 9, 17, 15, 11
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| T(n,k) = smallest m such that k * m = 1 (mod Prime(n)). Prime(n) is the n-th prime: A000040(n).
Contribution from Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010: (Start)
T(n,1) = 1
T(n,T(n,k)) = k
T(n,Prime(n)-1) = Prime(n)-1
1 <= m < Prime(n) (End)
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LINKS
| Franklin T. Adams-Watters, Table of n, a(n) for n = 1..4181 (primes less than 200)
Eric Weisstein's World of Mathematics, Modular Inverse
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EXAMPLE
| Table starts: 1; 1,2; 1,3,2,4; 1,4,5,2,3,6; ....
Contribution from Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010: (Start)
Table begins for the first nine primes 2,3,5,7,11,13,17,19,23:
1
1,2
1,3,2,4
1,4,5,2,3,6
1,6,4,3,9,2,8,7,5,10
1,7,9,10,8,11,2,5,3,4,6,12
1,9,6,13,7,3,5,15,2,12,14,10,4,11,8,16
1,10,13,5,4,16,11,12,17,2,7,8,3,15,14,6,9,18
1,12,8,6,14,4,10,3,18,7,21,2,16,5,20,13,19,9,17,15,11,22 (End)
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MATHEMATICA
| Flatten[Table[PowerMod[n, -1, p], {p, Prime[Range[9]]}, {n, p-1}]] [From Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010]
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CROSSREFS
| Cf. A124224, A102057, A000040, A006093 (row lengths).
Sequence in context: A163507 A003963 A003960 * A094193 A108712 A003602
Adjacent sequences: A124220 A124221 A124222 * A124224 A124225 A124226
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KEYWORD
| nonn,tabf
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 20 2006
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