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Search: id:A051864
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| A051864 |
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Sum of transposition distances (divided by 2) present in the permutation produced by inverses of 1..(p-1) computed in Zp, where p is n-th prime. |
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+0
1
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| 0, 0, 1, 4, 10, 25, 33, 46, 58, 97, 130, 247, 243, 310, 312, 417, 444, 729, 738, 654, 1007, 836, 968, 1095, 1623, 1603, 1720, 1652, 1997, 2143, 2872, 2786, 3123, 2920, 3069, 3534, 4103, 4654, 4130, 4933, 4434, 5355, 5576, 6959, 5915, 5788, 7440, 7994
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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a(n) = sum_of_transposition_distances(n) (See Maple code given below)
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EXAMPLE
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Inverses of 1 .. 10 in field Z11 are: 1,6,4,3,9,2,8,7,5,10 (e.g. 9*5 = 45 = 1 mod 11) if we count each inverse's "distance from its own position", we get 0+4+1+1+4+4+1+1+4+0 = 20, divided by 2 is 10, so a(5)=10 (11 is the fifth prime).
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MAPLE
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with(numtheory); sum_of_transposition_distances := proc(n) local p, i; p := ithprime(n); add(abs(op(2, op(1, msolve(i*x=1, p)))-i), i=1..(p-1))/2; end;
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CROSSREFS
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Sequence in context: A038783 A127070 A107961 this_sequence A111153 A111207 A113412
Adjacent sequences: A051861 A051862 A051863 this_sequence A051865 A051866 A051867
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Dec 14 1999
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