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 A080080 T(n,k) = length of longest carry sequence when adding k to n in binary representation, 1 <= k <= n (triangular array). 4
 1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 0, 3, 1, 1, 0, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 4, 1, 1, 0, 1, 1, 0, 0, 3, 3, 1, 1, 1, 2, 1, 1, 0, 4, 3, 3, 1, 2, 1, 1, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 4, 2, 2, 2, 2, 1, 1, 1, 3, 1, 1, 0, 3, 3, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS T(n,1) = A007814(n+1), T(n,n) = 1; for n>1: T(n,n-1) = A043545(n+1); T(n,k) <= A070940(n) = T(n, A080079(n)). T(n,k) = A050600(n+k,k) - 1. - Reinhard Zumkeller, Aug 03 2014 LINKS Reinhard Zumkeller, Rows n=1..150 of triangle, flattened EXAMPLE Triangle begins:               1             0   1           2   1   1         0   0   0   1       1   0   3   1   1     0   2   2   1   1   1   3   2   2   1   2   1   1 PROG (Haskell) import Data.Bits (xor, (.&.), shiftL) a080080 :: Int -> Int -> Int a080080 n k = addc n k 0 where    addc x y z | y == 0    = z - 1               | otherwise = addc (x `xor` y) (shiftL (x .&. y) 1) (z + 1) a080080_row n = map (a080080 n) [1..n] a080080_tabl = map a080080_row [1..] -- Reinhard Zumkeller, Apr 22 2013 CROSSREFS Cf. A050600. Sequence in context: A079677 A286564 A316359 * A093662 A284256 A250211 Adjacent sequences:  A080077 A080078 A080079 * A080081 A080082 A080083 KEYWORD nonn,tabl,nice AUTHOR Reinhard Zumkeller, Jan 26 2003 STATUS approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)