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A004515
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Generalized nim sum n + n in base 5.
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3
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0, 2, 4, 1, 3, 10, 12, 14, 11, 13, 20, 22, 24, 21, 23, 5, 7, 9, 6, 8, 15, 17, 19, 16, 18, 50, 52, 54, 51, 53, 60, 62, 64, 61, 63, 70, 72, 74, 71, 73, 55, 57, 59, 56, 58, 65, 67, 69, 66, 68, 100, 102, 104, 101, 103, 110
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OFFSET
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0,2
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COMMENTS
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I.e., double (mod 5) each digit (0->0, 1->2, 2->4, 3->1, 4->3) of the base-5 representation of n).
First 5^n terms of the sequence form a permutation s(n) of 0..5^n-1, n >= 1; the number of inversions of s(n) is 3*(25^n-5^n)/20 (i.e., 3, 90, 2325, 58500, 1464375, ...). - Gheorghe Coserea, Apr 23 2018
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LINKS
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FORMULA
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Generalized nim sum m + n in base q: write m and n in base q and add mod q with no carries, e.g., 5 + 8 in base 3 = "21" + "22" = "10" = 1.
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MATHEMATICA
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Array[FromDigits[IntegerDigits[#, 5] /. k_ :> Mod[2 k, 5], 5] &, 56, 0] (* Michael De Vlieger, Apr 27 2018 *)
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PROG
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(PARI)
a(n) = my(v=[0, 2, 4, 1, 3], b=#v); fromdigits(apply(d->v[d+1], digits(n, b)), b);
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CROSSREFS
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a(n) = A065257(n+1)-1 ("Quintal Queens" permutation).
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KEYWORD
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AUTHOR
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STATUS
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approved
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