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A127906 a(n) = (n in base 10) * (n in base 2).

%I A127906 #28 Sep 08 2022 08:45:29
%S A127906 0,1,20,33,400,505,660,777,8000,9009,10100,11121,13200,14313,15540,
%T A127906 16665,160000,170017,180180,190209,202000,212121,222420,232553,264000,
%U A127906 275025,286260,297297,310800,321929,333300,344441,3200000,3300033,3400340,3500385
%N A127906 a(n) = (n in base 10) * (n in base 2).
%C A127906 a(n) is a square for n=0 or a power of 4 (A000302). - _Michel Marcus_, Feb 20 2016
%C A127906 a(n) is a palindrome for n=0, 1, 3, 5, 7, 9, 33, 313, 455, 585, 819. Question: What is the next such n? If it exists it is greater than 10^9. - _Michel Marcus_, Feb 20 2016
%H A127906 Robert Israel, <a href="/A127906/b127906.txt">Table of n, a(n) for n = 0..10000</a>
%F A127906 a(n) = n*A007088(n). - _Michel Marcus_, Feb 21 2016
%e A127906 0*0, 1*1, 2*10, 3*11, 4*100, 5*101, 6*110, 7*111, 8*1000, 9*1001, 10*1010, ...
%e A127906 a(14) is 14*1110 = 15540.
%p A127906 A007088:= proc(n) option remember;
%p A127906    (n mod 2) + 10 * procname(floor(n/2))
%p A127906 end proc:
%p A127906 A007088(0):= 0:
%p A127906 seq(n*A007088(n),n=0..100); # _Robert Israel_, Feb 21 2016
%t A127906 Table[n*FromDigits[IntegerDigits[n, 2]], {n, 0, 30}] (* _Stefan Steinerberger_, May 05 2007 *)
%o A127906 (PARI) a(n) = n*subst(Pol(binary(n)), x, 10) ; \\ _Michel Marcus_, Feb 20 2016
%o A127906 (Magma) [Seqint(Intseq((n), 2))*n: n in [0..50]]; // _Vincenzo Librandi_, Feb 20 2016
%Y A127906 Cf. A007088.
%K A127906 nonn,base
%O A127906 0,3
%A A127906 Ivan Baroni (estatico04(AT)yahoo.com.br), Apr 05 2007
%E A127906 Corrected and extended by _Stefan Steinerberger_, May 05 2007
%E A127906 Offset set to 0 by _Michel Marcus_, Feb 20 2016