A182242 -id:A182242 - cp's OEIS frontend

A182243 a(0)=0, a(n) = (a(n-1) AND n) + n.

0, 1, 2, 5, 8, 5, 10, 9, 16, 9, 18, 13, 24, 21, 18, 17, 32, 17, 34, 21, 40, 21, 42, 25, 48, 41, 34, 29, 56, 53, 50, 49, 64, 33, 66, 37, 72, 37, 74, 41, 80, 41, 82, 45, 88, 53, 82, 49, 96, 81, 66, 53, 104, 85, 74, 57, 112, 105, 98, 93, 88, 85, 82, 81, 128, 65

Offset: 0

Alex Ratushnyak, Apr 20 2012

Reinhard Zumkeller, Table of n, a(n) for n = 0..8192=2^13
Eric Weisstein's World of Mathematics, AND
Wikipedia, Bitwise operation AND

Cf. A182242.

import Data.Bits ((.&.))
a182243 n = a182243_list !! n
a182243_list = map fst $ iterate f (0,1) where
   f (y,x) = ((x .&. y) + x, x + 1) :: (Integer,Integer)
-- Reinhard Zumkeller, Apr 23 2012

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

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

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

A182389 a(0)=1, a(n) = (a(n-1) + n) XOR n.

Original entry on oeis.org

1, 3, 7, 9, 9, 11, 23, 25, 41, 59, 79, 81, 81, 83, 111, 113, 145, 179, 215, 249, 281, 315, 327, 329, 377, 395, 447, 449, 449, 451, 511, 513, 513, 515, 519, 521, 521, 523, 535, 537, 617, 699, 719, 721, 721, 723, 815, 881, 913, 1011, 1047, 1145, 1177, 1275, 1287

Offset: 0

Alex Ratushnyak, Apr 27 2012

a(n) >= n.

a(n) >= a(n-1). - Daniel Leary, Aug 21 2016

			a(5) = (a(4)+5) XOR 5 = (9+5) XOR 5 = 14 XOR 5 = 11.

Paolo Xausa, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Ivan Panchenko)

Cf. A182242, A182247, A237054.

Module[{n = 0}, NestList[BitXor[++n, # + n] &, 1, 100]] (* Paolo Xausa, Nov 26 2024 *)

a=1
for i in range(1,55):
    print(a, end=',')
    a += i
    a ^= i

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

A237054 a(1)=1, a(n) = (a(n-1) + n) XOR n.

Original entry on oeis.org

1, 1, 7, 15, 17, 17, 31, 47, 49, 49, 55, 79, 81, 81, 111, 111, 145, 177, 215, 255, 257, 257, 271, 319, 321, 321, 327, 383, 385, 385, 447, 511, 513, 513, 519, 527, 529, 529, 543, 623, 689, 753, 823, 847, 849, 849, 943, 1007, 1041, 1137, 1175, 1279, 1281, 1281

Offset: 1

Alex Ratushnyak, Feb 03 2014

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A182389, A182242.

Module[{n = 1}, NestList[BitXor[++n, # + n] &, 1, 100]] (* Paolo Xausa, Nov 26 2024 *)

a=1
for n in range(2, 77):
  print(a, end=', ')
  a = (a+n) ^ n

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

A330581 a(0) = 2; thereafter a(n) = a(n - 1)^n + 1.

Original entry on oeis.org

2, 3, 10, 1001, 1004006004002, 1020191144865623440455270145683555422808365843606721760320033

Offset: 0

David Johnson-Davies, Dec 18 2019

nonn

Note that this could be extended backwards to a(-1), and any nonzero value x for a(-1) would work, since x^0 + 1 = 2.

David Johnson-Davies, Recursive functions without a base case

Cf. A000522, A182242.

(defun a (n) (+ (if (zerop n) 1 (expt (a (- n 1)) n)) 1))

a:= proc(n) option remember; `if`(n<0, %,
      1 + a(n-1)^n)
    end:
seq(a(n), n=0..5);  # Alois P. Heinz, Dec 18 2019

a[0] = 2; a[n_] := a[n] = a[n - 1]^n + 1; Array[a, 6, 0] (* Amiram Eldar, Dec 19 2019 *)
nxt[{n_,a_}]:={n+1,a^(n+1)+1}; NestList[nxt,{0,2},5][[;;,2]] (* Harvey P. Dale, Dec 10 2023 *)

a(n) = if(n==0, 2, a(n-1)^n+1) \\ Felix Fröhlich, Dec 18 2019

Edited by N. J. A. Sloane, Dec 27 2019

cp's OEIS Frontend

A182243 a(0)=0, a(n) = (a(n-1) AND n) + n.

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A182389 a(0)=1, a(n) = (a(n-1) + n) XOR n.

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A237054 a(1)=1, a(n) = (a(n-1) + n) XOR n.

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A330581 a(0) = 2; thereafter a(n) = a(n - 1)^n + 1.

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