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A309991
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Balanced quinary (base 5) enumeration (or balanced quinary representation) of integers, write n in quinary, and then replace 3's with (-2)'s and 4's with (-1)'s.
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4
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0, 1, 2, -2, -1, 5, 6, 7, 3, 4, 10, 11, 12, 8, 9, -10, -9, -8, -12, -11, -5, -4, -3, -7, -6, 25, 26, 27, 23, 24, 30, 31, 32, 28, 29, 35, 36, 37, 33, 34, 15, 16, 17, 13, 14, 20, 21, 22, 18, 19, 50, 51, 52, 48, 49, 55, 56, 57, 53, 54, 60, 61, 62, 58, 59, 40, 41
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listen;
history;
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OFFSET
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0,3
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COMMENTS
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This sequence, like the balanced ternary sequence, will eventually include every integer exactly once.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..15624
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 0,
5*a(iquo(n, 5))+mods(n, 5))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Aug 26 2019
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MATHEMATICA
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Table[FromDigits[IntegerDigits[n, 5]/.{3->-2, 4->-1}, 5], {n, 0, 120}] (* Harvey P. Dale, Sep 05 2020 *)
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PROG
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(PARI) a(n) = subst(Pol(apply(d->if(d>2, d-5, d), digits(n, 5)), 'x), 'x, 5) \\ Andrew Howroyd, Aug 26 2019
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CROSSREFS
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Cf. A117966.
Column k=2 of A319047.
Sequence in context: A056857 A175579 A129100 * A162382 A325580 A127082
Adjacent sequences: A309988 A309989 A309990 * A309992 A309993 A309994
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KEYWORD
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sign,base
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AUTHOR
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Jackson Haselhorst, Aug 26 2019
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STATUS
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approved
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