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Integers n > 0 such that n XOR 30*n = 31*n.
5

%I #14 May 23 2017 09:25:08

%S 1,2,4,8,16,32,33,64,65,66,128,129,130,132,256,257,258,260,264,512,

%T 513,514,516,520,528,1024,1025,1026,1028,1032,1040,1056,1057,2048,

%U 2049,2050,2052,2056,2064,2080,2081,2112,2113,2114,4096,4097,4098,4100,4104,4112

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

%H Ivan Neretin, <a href="/A115423/b115423.txt">Table of n, a(n) for n = 1..10000</a>

%F This sequence also seems to satisfy:

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

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

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

%F a(A003520(n+4)) = 2^n. - _Gheorghe Coserea_, Nov 11 2016

%t Select[Range[4200],BitXor[#,30#]==31#&] (* _Harvey P. Dale_, May 23 2017 *)

%o (Perl)

%o $cnt=0;

%o foreach(1..4_000){

%o print ++$cnt," $_\n" if ((30*$_)^$_)==31*$_;

%o }

%o # _Ivan Neretin_, Nov 11 2016

%o (PARI) isok(n) = bitxor(n, 30*n) == 31*n; \\ _Michel Marcus_, Nov 11 2016

%Y Cf. A003714 (Fibbinary numbers), A048715, A048718, A115422, A115424.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 22 2006