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

%I A115423 #14 May 23 2017 09:25:08
%S A115423 1,2,4,8,16,32,33,64,65,66,128,129,130,132,256,257,258,260,264,512,
%T A115423 513,514,516,520,528,1024,1025,1026,1028,1032,1040,1056,1057,2048,
%U A115423 2049,2050,2052,2056,2064,2080,2081,2112,2113,2114,4096,4097,4098,4100,4104,4112
%N A115423 Integers n > 0 such that n XOR 30*n = 31*n.
%H A115423 Ivan Neretin, <a href="/A115423/b115423.txt">Table of n, a(n) for n = 1..10000</a>
%F A115423 This sequence also seems to satisfy:
%F A115423 3*a(n) XOR 21*a(n) = 22*a(n);
%F A115423 5*a(n) XOR 19*a(n) = 22*a(n);
%F A115423 6*a(n) XOR 19*a(n) = 21*a(n); etc.
%F A115423 a(A003520(n+4)) = 2^n. - _Gheorghe Coserea_, Nov 11 2016
%t A115423 Select[Range[4200],BitXor[#,30#]==31#&] (* _Harvey P. Dale_, May 23 2017 *)
%o A115423 (Perl)
%o A115423 $cnt=0;
%o A115423 foreach(1..4_000){
%o A115423     print ++$cnt," $_\n" if ((30*$_)^$_)==31*$_;
%o A115423 }
%o A115423 # _Ivan Neretin_, Nov 11 2016
%o A115423 (PARI) isok(n) = bitxor(n, 30*n) == 31*n; \\ _Michel Marcus_, Nov 11 2016
%Y A115423 Cf. A003714 (Fibbinary numbers), A048715, A048718, A115422, A115424.
%K A115423 nonn
%O A115423 1,2
%A A115423 _Paul D. Hanna_, Jan 22 2006