A115424 Integers n > 0 such that n XOR 62*n = 63*n.

1, 2, 4, 8, 16, 32, 64, 65, 128, 129, 130, 256, 257, 258, 260, 512, 513, 514, 516, 520, 1024, 1025, 1026, 1028, 1032, 1040, 2048, 2049, 2050, 2052, 2056, 2064, 2080, 4096, 4097, 4098, 4100, 4104, 4112, 4128, 4160, 4161, 8192, 8193, 8194, 8196, 8200, 8208

Offset: 1

Author

Paul D. Hanna, Jan 22 2006

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003714 (Fibbinary numbers), A048715, A048718, A115422, A115423.

Programs

Mathematica

Select[Range[8300],BitXor[#,62 #]==63 #&] (* Harvey P. Dale, Oct 31 2021 *)

PARI

isok(n) = bitxor(n, 62*n) == 63*n; \\ Michel Marcus, Nov 11 2016

Perl

$cnt=0;
foreach(1..8_000){
    print ++$cnt," $\n" if ((62*$)^$)==63*$;
}
# Ivan Neretin, Nov 11 2016

Formula

This sequence also seems to satisfy:

3*a(n) XOR 41*a(n) = 42*a(n);

5*a(n) XOR 35*a(n) = 38*a(n);

6*a(n) XOR 35*a(n) = 37*a(n);

7*a(n) XOR 35*a(n) = 36*a(n); etc.