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A320487 a(0) = 1; thereafter a(n) is obtained by applying the "delete multiple digits" map m -> A320485(m) to 2*a(n-1).

%I A320487 #45 Aug 03 2025 23:39:45
%S A320487 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,3,6,12,
%T A320487 24,48,96,192,384,768,1536,3072,61,1,2,4,8,16,32,64,128,256,512,1024,
%U A320487 2048,4096,8192,16384,32768,3,6,12,24,48,96,192,384,768,1536,3072,61,1
%N A320487 a(0) = 1; thereafter a(n) is obtained by applying the "delete multiple digits" map m -> A320485(m) to 2*a(n-1).
%C A320487 In short, double the previous term and delete any digits appearing more than once.
%C A320487 Periodic with period 28.
%C A320487 Using the variant A320486 yields the same sequence, since the empty string never occurs. - _M. F. Hasler_, Oct 24 2018
%C A320487 Conjecture: If we start with any nonnegative integer and repeatedly double and apply the "delete multiple digits" map m -> A320485(m), we eventually reach 0 or 1 (see A323835). - _N. J. A. Sloane_, Feb 03 2019
%D A320487 Eric Angelini, Posting to Sequence Fans Mailing List, Oct 24 2018
%H A320487 N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence)
%e A320487 2*32768 = 65536 -> 3 since we delete the multiple digits 6 and 5.
%e A320487 2*61 = 122 -> 1 since we delete the multiple 2's.
%t A320487 a[0] = 1;a[n_] := a[n] = FromDigits[First /@ Select[ Tally[IntegerDigits[2 a[n - 1]]], #[[2]] == 1 &]];Table[a[n], {n, 0, 56}] (* _Stan Wagon_, Nov 17 2018 *)
%o A320487 (PARI) A=[2];for(i=1,99,A=concat(A,A320486(A[#A]*2)));A \\ _M. F. Hasler_, Oct 24 2018
%Y A320487 Cf. A000079, A065243, A320485, A323830.
%Y A320487 See A035615 for a classic related base-2 sequence.
%K A320487 nonn,base
%O A320487 0,2
%A A320487 _N. J. A. Sloane_, Oct 24 2018, following a suggestion from _Eric Angelini_