A182242 a(0)=0, a(n) = (a(n-1) + n) AND n.

0, 1, 2, 1, 4, 1, 6, 5, 8, 1, 10, 1, 12, 9, 6, 5, 16, 1, 18, 1, 20, 1, 22, 5, 24, 17, 10, 1, 28, 25, 22, 21, 32, 1, 34, 1, 36, 1, 38, 5, 40, 1, 42, 1, 44, 9, 38, 5, 48, 33, 18, 1, 52, 33, 22, 5, 56, 49, 42, 33, 28, 25, 22, 21, 64, 1, 66, 1, 68, 1, 70, 5, 72, 1

Offset: 0

Author

Alex Ratushnyak, Apr 20 2012

Keywords

• nonn
• base
• look

Comments

Indices of 1's (that is, n's such that a(n)=1)

1, 3, 5, 9, 11, 17, 19, 21, 27, 33, 35, 37, 41, 43, 51, 65, 67, 69, 73, 75, 81, 83, 85, 91, 99, 107, 129, 131, 133, 137, 139, 145, 147, 149, 155, 161, 163, 165, 169, 171, 179, 195, 203, 211, 219, 257, 259, 261, 265, etc.

Indices of 5's:

7, 15, 23, 39, 47, 55, 71, 79, 87, 103, 111, 119, 135, 143, 151, 167, 175, 183, 199, 207, 215, 231, 239, 263, 271, 279, 295, 303, 311, 327, 335, 343, 359, 367, 375, 391, 399, 407, 423, 431, 439, 455, 463, 471, 495, 519, etc.

Indices of 9's:

13, 45, 77, 141, 173, 269, 301, 333, 525, 557, 589, 653, 685, 1037, 1069, 1101, 1165, 1197, 1293, 1325, 1357, 2061, 2093, 2125, 2189, 2221, 2317, 2349, 2381, 2573, 2605, 2637, 2701, 2733, 4109, 4141, 4173, 4237, 4269, etc.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, AND
• Wikipedia, Bitwise operation AND

Crossrefs

Cf. A182243.

Programs

Haskell

import Data.Bits ((.&.))
a182242 n = a182242_list !! n
a182242_list = map fst $ iterate f (0,1) where
   f (y,x) = ((x + y) .&. x, x + 1) :: (Integer,Integer)
-- Reinhard Zumkeller, Apr 23 2012

Mathematica

Join[{t = 0}, Table[t = BitAnd[(t + n), n], {n, 100}]] (* T. D. Noe, Apr 21 2012 *)

Python

a=0
for i in range(1,511):
    print(a, end=',')
    a += i
    a &= i

Formula

a(0)=0, a(n)=(a(n-1)+n) AND n, where AND is the bitwise logical AND operator.