A115422 Integers n > 0 such that n XOR 20*n = 21*n.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 33, 36, 48, 64, 65, 66, 67, 72, 73, 96, 97, 128, 129, 130, 131, 132, 134, 144, 146, 192, 193, 194, 195, 256, 257, 258, 259, 260, 262, 264, 265, 268, 288, 289, 292, 384, 385, 386, 387, 388, 390, 512, 513, 514, 515, 516, 518

Offset: 1

Author

Paul D. Hanna, Jan 22 2006

Keywords

• nonn

Comments

n is in the sequence iff 2*n is in the sequence. - Robert Israel, Nov 11 2016

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10203

Crossrefs

Cf. A003714 (Fibbinary numbers), A048715, A048718, A115423, A115424.

Programs

Maple

select(n -> Bits:-Xor(n,20*n)=21*n, [$1..1000]); # Robert Israel, Nov 11 2016

Mathematica

Select[Range[600],BitXor[#,20#]==21#&] (* Harvey P. Dale, Apr 21 2018 *)

PARI

isok(n) = bitxor(n, 20*n) == 21*n; \\ Michel Marcus, Nov 11 2016

Perl

$cnt=0;
foreach(1..1_000){
    print ++$cnt," $\n" if ((20*$)^$)==21*$;
}
# Ivan Neretin, Nov 10 2016

Formula

This sequence also seems to satisfy:

5*a(n) XOR 16*a(n) = 21*a(n);

5*a(n) XOR 17*a(n) = 20*a(n); etc.

a(A224809(n+4)) = 2^n. - Gheorghe Coserea, Nov 11 2016