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A050605
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Column/row 2 of A050602: a(n) = add3c(n,2).
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8
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0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 4, 4, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 5, 5, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 3, 3, 0, 0, 1, 1, 0, 0, 2, 2
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OFFSET
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0,7
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COMMENTS
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It seems that (n - Sum_{k=1..n} a(k) )/log(n) is bounded. - Benoit Cloitre, Oct 03 2002
2^a(n-1) is the highest power of 2 dividing the triangular number A000217(n) = n*(n+1)/2, for n >= 1. - Benoit Cloitre, Oct 03 2002 [corrected and rewritten by Wolfdieter Lang, Nov 21 2019]
a(n) is the number of trailing 0's in the binary reflected Gray code of n+1 (A014550). - Amiram Eldar, May 15 2021
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LINKS
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FORMULA
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MAPLE
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with(Bits): add3c := proc(a, b) option remember; `if`(0 = And(a, b), 0, 1 + add3c(Xor(a, b), 2*And(a, b))) end: A050605 := n -> add3c(n, 2):
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MATHEMATICA
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PROG
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(PARI) a(n)=valuation(n*(n+1)/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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