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

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 61, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 61, 1

Offset: 0

Author

N. J. A. Sloane, Oct 24 2018, following a suggestion from Eric Angelini

Keywords

• nonn
• base

Comments

In short, double the previous term and delete any digits appearing more than once.

Periodic with period 28.

Using the variant A320486 yields the same sequence, since the empty string never occurs. - M. F. Hasler, Oct 24 2018

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

Examples

			2*32768 = 65536 -> 3 since we delete the multiple digits 6 and 5.
2*61 = 122 -> 1 since we delete the multiple 2's.
		

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Oct 24 2018

Links

• N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Cf. A000079, A065243, A320485, A323830.

See A035615 for a classic related base-2 sequence.

Programs

Mathematica

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 *)

PARI

A=[2];for(i=1,99,A=concat(A,A320486(A[#A]*2)));A \\ M. F. Hasler, Oct 24 2018