A115793 - OEIS

%I #18 Jul 31 2021 14:57:46

%S 0,1,2,4,5,8,10,13,16,17,20,26,29,32,33,34,40,45,52,58,64,65,66,68,69,

%T 77,80,81,90,93,104,116,128,129,130,132,133,136,138,154,157,160,161,

%U 162,180,186,205,208,209,232,256,257,258,260,261,264,266,269,272,273

%N Integers i such that i XOR 10i = 11i.

%C XOR is A003987.

%C Also: numbers i such that binomial(11*i,i) is odd. - _Zak Seidov_, Aug 08 2010

%C 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.

%C n is a term if and only if 2*n is a term. - _Robert Israel_, Apr 14 2020

%H Robert Israel, <a href="/A115793/b115793.txt">Table of n, a(n) for n = 1..10000</a>

%H A. M. Hinz, <a href="http://www.jstor.org/stable/2324061">Pascal's Triangle and the Tower of Hanoi</a>, Am. Math. Monthly 99 (6) (1992) 538-544.

%H <a href="/index/Con#CongruXOR">Index entries for sequences defined by congruent products under XOR</a>

%e 5 is a member because:

%e in binary, 5 = 000101

%e in binary 50 = 110010

%e in binary 55 = 110111

%e and 000101 XOR 110010 = 110111.

%p filter:= proc(n) Bits:-Xor(n,10*n)=11*n end proc:

%p select(filter, [$0..1000]); # _Robert Israel_, Apr 14 2020

%t Select[Range[0,300],BitXor[#,10#]==11#&] (* _Harvey P. Dale_, Jul 31 2021 *)

%o (PARI) is(n)=bitxor(n,10*n)==11*n \\ _Charles R Greathouse IV_, Apr 14 2020

%Y Cf. A115794 shows this sequence in binary.

%K nonn,look

%O 1,3

%A _Antti Karttunen_, Feb 01 2006

%E Definition clarified by _N. J. A. Sloane_, Aug 14 2010

%E Offset changed to 1 by _Robert Israel_, Apr 14 2020