A269633 Numbers whose arithmetic derivative is equal to their BCR, where BCR = A036044, binary-complement-and-reverse = take one's complement then reverse bit order.

1, 9, 21, 93, 381, 6596, 20995, 24573, 57823, 62359, 98756, 208148, 393213, 400844, 405788, 418756, 1572861, 6460508

Offset: 1

Author

Paolo P. Lava, Mar 02 2016

Keywords

• nonn
• base
• more

Examples

			9 is 1001 in base 2; complement: 0110; reverse: 0110 that is 6 in base 10 and 9' = 6;
21 is 10101 in base 2; complement: 01010; reverse: 01010 that is 10 in base 10 and 21' = 10.
		

Crossrefs

Cf. A003415, A036044.

Programs

Maple

P:=proc(q) local a,b, k,n,p;
for n from 1 to q do a:=convert(n,base,2); b:=0;
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;
if b=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]) then print(n); fi;
od; end: P(10^6);

Mathematica

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 *)

Formula

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