OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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
KEYWORD
mult,easy,nonn
AUTHOR
Henry Bottomley, May 02 2000
STATUS
approved