A115423 Integers n > 0 such that n XOR 30*n = 31*n.

1, 2, 4, 8, 16, 32, 33, 64, 65, 66, 128, 129, 130, 132, 256, 257, 258, 260, 264, 512, 513, 514, 516, 520, 528, 1024, 1025, 1026, 1028, 1032, 1040, 1056, 1057, 2048, 2049, 2050, 2052, 2056, 2064, 2080, 2081, 2112, 2113, 2114, 4096, 4097, 4098, 4100, 4104, 4112

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, A115424.

Programs

Mathematica

Select[Range[4200],BitXor[#,30#]==31#&] (* Harvey P. Dale, May 23 2017 *)

PARI

isok(n) = bitxor(n, 30*n) == 31*n; \\ Michel Marcus, Nov 11 2016

Perl

$cnt=0;
foreach(1..4_000){
    print ++$cnt," $\n" if ((30*$)^$)==31*$;
}
# Ivan Neretin, Nov 11 2016

Formula

This sequence also seems to satisfy:

3*a(n) XOR 21*a(n) = 22*a(n);

5*a(n) XOR 19*a(n) = 22*a(n);

6*a(n) XOR 19*a(n) = 21*a(n); etc.

a(A003520(n+4)) = 2^n. - Gheorghe Coserea, Nov 11 2016