A080080 - OEIS

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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

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

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