A115793 Integers i such that i XOR 10i = 11i.

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, 77, 80, 81, 90, 93, 104, 116, 128, 129, 130, 132, 133, 136, 138, 154, 157, 160, 161, 162, 180, 186, 205, 208, 209, 232, 256, 257, 258, 260, 261, 264, 266, 269, 272, 273

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.

Index entries for sequences defined by congruent products under XOR

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

Cf. A115794 shows this sequence in binary.

Sequence in context: A186349 A304360 A072437 * A076614 A227800 A144876

Adjacent sequences: A115790 A115791 A115792 * A115794 A115795 A115796

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