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A332202
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Largest k >= 0 such that 3^k divides 2^(2^n-1) + 1.
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2
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0, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1
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OFFSET
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0,3
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COMMENTS
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Behaves like a mixture of 2-adic and 3-adic ruler function, cf. formula.
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 0 since 2^(2^0-1) + 1 = 2^0 + 1 = 2 is not divisible by 3.
a(1) = 1 since 2^(2^1-1) + 1 = 2^1 + 1 = 3 is divisible just once by 3.
a(2) = 2 since 2^(2^2-1) + 1 = 2^3 + 1 = 9 is divisible by 3^2.
a(3) = 1 since 2^(2^4-1) + 1 = 2^15 + 1 = 32769 is divisible only once by 3.
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PROG
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(PARI) apply( {A332202(n)=if(bittest(n, 0), 1, n, valuation(n\2, 3)+2)}, [0..99])
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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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