A038713 a(n) = n XOR (n-1), i.e., nim-sum of sequential pairs, written in binary.

1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 11111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 111111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 11111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 1111111, 1, 11, 1, 111, 1

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Nim-sums

Formula

a(n) = (10^A001511(n) - 1)/(10 - 1).

Multiplicative with a(2^e) = (10^(e+1) - 1)/9, a(p^e) = 1 if p odd.

G.f.: Sum_{k>=0} 10^k * x^(2^k) / (1 - x^(2^k)). - Ilya Gutkovskiy, Dec 15 2020

Dirichlet g.f.: zeta(s) * 2^s/(2^s - 10). - Amiram Eldar, Sep 21 2023

Example

a(6) = 11 because 110 XOR 101 = 11 base 2.

Mathematica

Table[(10^IntegerExponent[2*n, 2] - 1)/9, {n, 100}] (* Vincenzo Librandi, Mar 11 2013 *)

Prog

(PARI) a(n)=if(n<1, 0, (10^(valuation(n, 2)+1)-1)/9) /* Michael Somos, Apr 28 2005 */
(Magma) [(10^(Valuation(n, 2)+1)-1)/9: n in [1..70]]; // Vincenzo Librandi, Mar 11 2013

Crossrefs

Cf. A038712 translated to binary, A001511 translated to unary (repeated 1's).

Sequence in context: A289092 A104490 A164851 * A130556 A277932 A290676

Adjacent sequences: A038710 A038711 A038712 * A038714 A038715 A038716

Keyword

mult,easy,nonn

Author

Henry Bottomley, May 02 2000

Status

approved