A080080 T(n,k) = length of longest carry sequence when adding k to n in binary representation, 1 <= k <= n (triangular array).

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

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

Index entries for sequences related to binary expansion of n

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 A354841

Adjacent sequences: A080077 A080078 A080079 * A080081 A080082 A080083

Keyword

nonn,tabl,nice

Author

Reinhard Zumkeller, Jan 26 2003

Status

approved