A182388 a(0) = 1, a(n) = (a(n-1) XOR n) + n.

1, 1, 5, 9, 17, 25, 37, 41, 41, 41, 45, 49, 73, 81, 109, 113, 113, 113, 117, 121, 129, 169, 213, 217, 217, 217, 221, 225, 281, 289, 349, 353, 353, 353, 357, 361, 369, 377, 389, 457, 521, 585, 653, 721, 809, 817, 845, 913, 977, 1041, 1109, 1177, 1249

Offset

0,3

Comments

a(n)>=n.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, XOR

Wikipedia, Bitwise operation XOR

Formula

a(0) = 1, a(n) = (a(n-1) XOR n) + n, where XOR is the bitwise exclusive-OR operator.

Example

a(5) = (a(4) XOR 5) + 5 = (17 XOR 5) + 5 = 20 + 5 = 25.

Mathematica

FoldList[BitXor[#, #2] + #2 &, 1, Range[100]] (* Paolo Xausa, Apr 16 2025 *)

Prog

(Python)
a=1
for i in range(1, 55):
    print(a, end=', ')
    a ^= i
    a += i
(Haskell)
import Data.Bits (xor)
a182388 n = a182388_list !! n
a182388_list = f 0 1 where
   f x y = y' : f (x + 1) y' :: [Integer] where y' = (x `xor` y) + x
-- Reinhard Zumkeller, Apr 29 2012

Crossrefs

Cf. A182243, A182248.

Sequence in context: A054278 A210978 A211434 * A080335 A351837 A089109

Adjacent sequences: A182385 A182386 A182387 * A182389 A182390 A182391

Keyword

nonn,base

Author

Alex Ratushnyak, Apr 27 2012

Status

approved