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A275019
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2-adic valuation of tetrahedral numbers C(n+2,3) = n(n+1)(n+2)/6 = A000292.
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2
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0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 4, 3, 4, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 5, 4, 5, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 4, 3, 4, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 6, 5, 6, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 4, 3, 4, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 5, 4, 5, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 4
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OFFSET
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1,2
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COMMENTS
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The subsequence of every other term (a(2n-1), n >= 1) is the ruler sequence A007814 = (0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, ...), in particular every fourth term is zero. The nonzero terms among them, a(4n-1) = A007814(2n) (n >= 1) have both their neighbors equal to one more than themselves, a(4n-2) = a(4n) = a(4n-1) + 1 = A007814(2n) + 1.
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LINKS
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FORMULA
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G.f.: (1+x+x^2)*Sum_{k>=1} x^(2^k-2)/(1-x^(2^k)) - 1/(1-x). (End)
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MAPLE
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seq(padic:-ordp(n*(n+1)*(n+2)/6, 2), n=1..100); # Robert Israel, Dec 04 2016
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PROG
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(PARI) a(n)=valuation(n*(n+1)*(n+2)/6, 2)
(Magma) [Valuation(n*(n+1)*(n+2)/6, 2): n in [1..100]]; // Vincenzo Librandi, Dec 04 2016
(Python)
def A275019(n): return (~(m:=n*(n+1)*(n+2)//6)& m-1).bit_length() # Chai Wah Wu, Jul 07 2022
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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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