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

1,2

Links

Table of n, a(n) for n=1..18.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A003415, A036044.

Sequence in context: A147480 A146396 A146681 * A279389 A359022 A222809

Adjacent sequences: A269630 A269631 A269632 * A269634 A269635 A269636

Keyword

nonn,base,more

Author

Paolo P. Lava, Mar 02 2016

Status

approved