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A302338
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a(n) = 3*n + 2^v(n) where v(n) denotes the 2-adic valuation of n.
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1
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4, 8, 10, 16, 16, 20, 22, 32, 28, 32, 34, 40, 40, 44, 46, 64, 52, 56, 58, 64, 64, 68, 70, 80, 76, 80, 82, 88, 88, 92, 94, 128, 100, 104, 106, 112, 112, 116, 118, 128, 124, 128, 130, 136, 136, 140, 142, 160, 148, 152, 154, 160, 160, 164, 166, 176, 172, 176, 178
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OFFSET
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1,1
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COMMENTS
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The sequence can be seen as a variant of the Collatz map (A006370) where we perform only tripling steps.
If the 3x+1 (or Collatz) conjecture is true, then for any n > 0, A006667(n) is the least k such that a^k(n) is a power of two (where a^k denotes the k-th iterate of the sequence).
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LINKS
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FORMULA
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a(2*n) = 2*a(n).
a(2*k + 1) = A006370(2*k + 1) for any k >= 0.
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EXAMPLE
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a(42) = 3*42 + 2^1 = 128.
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MAPLE
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seq(3*n+2^padic:-ordp(n, 2), n=1..100); # Robert Israel, Apr 29 2018
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MATHEMATICA
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PROG
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(PARI) a(n) = 3*n + 2^valuation(n, 2)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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