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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
1, 9, 21, 93, 381, 6596, 20995, 24573, 57823, 62359, 98756, 208148, 393213, 400844, 405788, 418756, 1572861, 6460508 (list; graph; refs; listen; history; text; internal format)
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 A222809 A230648

Adjacent sequences:  A269630 A269631 A269632 * A269634 A269635 A269636

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Mar 02 2016

STATUS

approved

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Last modified September 28 09:11 EDT 2022. Contains 357068 sequences. (Running on oeis4.)