A269633 - OEIS

%I #11 Apr 13 2019 14:24:09

%S 1,9,21,93,381,6596,20995,24573,57823,62359,98756,208148,393213,

%T 400844,405788,418756,1572861,6460508

%N Numbers whose arithmetic derivative is equal to their BCR, where BCR = A036044, binary-complement-and-reverse = take one's complement then reverse bit order.

%F Solution of the equation A003415(n) = A036044(n).

%e 9 is 1001 in base 2; complement: 0110; reverse: 0110 that is 6 in base 10 and 9' = 6;

%e 21 is 10101 in base 2; complement: 01010; reverse: 01010 that is 10 in base 10 and 21' = 10.

%p P:=proc(q) local a,b, k,n,p;

%p for n from 1 to q do a:=convert(n,base,2); b:=0;

%p for k from 1 to nops(a) do if a[k]=0 then a[k]:=1 else a[k]:=0; fi; b:=2*b+a[k]; od;

%p if b=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]) then print(n); fi;

%p od; end: P(10^6);

%t f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]; g[n_] := FromDigits[Reverse[IntegerDigits[n, 2] /. {1 -> 0, 0 -> 1}], 2]; Select[Range[10^6], f@ # == g@ # &] (* _Michael De Vlieger_, Mar 03 2016, after _Michael Somos_ at A003415 and _Harvey P. Dale_ at A036044 *)

%Y Cf. A003415, A036044.

%K nonn,base,more

%O 1,2

%A _Paolo P. Lava_, Mar 02 2016