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

0,3

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A182243.

Sequence in context: A146386 A305098 A128099 * A261605 A239093 A263453

Adjacent sequences: A182239 A182240 A182241 * A182243 A182244 A182245

Keyword

nonn,base,look

Author

Alex Ratushnyak, Apr 20 2012

Status

approved