OFFSET
1,3
COMMENTS
XOR is A003987.
Also: numbers i such that binomial(11*i,i) is odd. - Zak Seidov, Aug 08 2010
The equivalence between the definition as those i for which 11*i is the carryless sum of i and 10*i and the alternative that the binomial coefficient be odd follows from Lucas' theorem on binomial coefficients.
n is a term if and only if 2*n is a term. - Robert Israel, Apr 14 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
A. M. Hinz, Pascal's Triangle and the Tower of Hanoi, Am. Math. Monthly 99 (6) (1992) 538-544.
EXAMPLE
5 is a member because:
in binary, 5 = 000101
in binary 50 = 110010
in binary 55 = 110111
and 000101 XOR 110010 = 110111.
MAPLE
filter:= proc(n) Bits:-Xor(n, 10*n)=11*n end proc:
select(filter, [$0..1000]); # Robert Israel, Apr 14 2020
MATHEMATICA
Select[Range[0, 300], BitXor[#, 10#]==11#&] (* Harvey P. Dale, Jul 31 2021 *)
PROG
(PARI) is(n)=bitxor(n, 10*n)==11*n \\ Charles R Greathouse IV, Apr 14 2020
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Feb 01 2006
EXTENSIONS
Definition clarified by N. J. A. Sloane, Aug 14 2010
Offset changed to 1 by Robert Israel, Apr 14 2020
STATUS
approved