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A305418
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Permutation of nonnegative integers: a(1) = 0, a(2n) = 1 + 2*a(n), a(2n+1) = 2*a(A305422(2n+1)).
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5
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0, 1, 2, 3, 6, 5, 4, 7, 10, 13, 8, 11, 16, 9, 14, 15, 30, 21, 32, 27, 12, 17, 34, 23, 64, 33, 22, 19, 18, 29, 128, 31, 258, 61, 36, 43, 256, 65, 38, 55, 512, 25, 130, 35, 46, 69, 1024, 47, 20, 129, 62, 67, 66, 45, 2048, 39, 70, 37, 4096, 59, 8192, 257, 26, 63, 54, 517, 16384, 123, 24, 73, 16386, 87, 32768, 513, 142, 131, 8194, 77, 132, 111, 48, 1025, 42, 51
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OFFSET
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1,3
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COMMENTS
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This is GF(2)[X] analog of A156552. Note the indexing: the domain starts from 1, while the range includes also zero.
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LINKS
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FORMULA
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a(1) = 0, a(2n) = 1 + 2*a(n), a(2n+1) = 2*a(A305422(2n+1)).
For all n >= 1:
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PROG
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(PARI)
A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305419(n) = if(n<3, 1, my(k=n-1); while(k>1 && !A091225(k), k--); (k));
A305422(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))), x, 2)); for(i=1, #f~, f[i, 1] = Pol(binary(A305419(f[i, 1])))); fromdigits(Vec(factorback(f))%2, 2); };
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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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