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A268182
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A solution to a(n+1) in {a(n)+2, a(n)-2, a(n)*2, a(n)/2} which is a rearrangement of the natural numbers.
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0
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2, 1, 3, 6, 4, 8, 10, 5, 7, 9, 11, 22, 20, 18, 16, 14, 12, 24, 26, 13, 15, 17, 19, 21, 23, 25, 27, 54, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 56, 58, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59
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OFFSET
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1,1
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COMMENTS
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Use algorithm: when a(n)=2k+1 2k+1 -> 4k+2, 4k, 4k-2, 4k-4, ...-> 2k+2 -> *2-> 4k+4 +2-> 4k+6 -> /2-> 2k+3, 2k+5, +2... ->4k+7. This covers all numbers between 2k+1 and 4k+7 and then the algorithm can be reapplied.
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LINKS
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FORMULA
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a(n) = n if and only if n is a positive term of A168616. Also, for j > 2, a(n) < a(2^j - 5) if and only if n < 2^j - 5. - Rick L. Shepherd, May 22 2016
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PROG
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(PARI) {get_next_stage(v) = local(k = (v[#v] - 1)/2);
forstep(m = 2*v[#v], 2*k + 2, -2, v = concat(v, m));
v = concat(v, [2*v[#v], 4*k + 6]);
forstep(m = v[#v]/2, 4*k + 7, 2, v = concat(v, m)); v}
a = [2, 1, 3]; \\ code assumes last entry here is odd.
\\ n-th call to function returns 2^(n + 2) more terms
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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