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A320487
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a(0) = 1; thereafter a(n) is obtained by applying the "delete multiple digits" map m -> A320485(m) to 2*a(n-1).
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33
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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
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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Eric Angelini, Posting to Sequence Fans Mailing List, Oct 24 2018
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LINKS
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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)
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EXAMPLE
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2*32768 = 65536 -> 3 since we delete the multiple digits 6 and 5.
2*61 = 122 -> 1 since we delete the multiple 2's.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = FromDigits[First /@ Select[ Tally[IntegerDigits[2 a[n - 1]]], #[[2]] == 1 &]] /* Stan Wagon, Nov 17 2018_ */
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PROG
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CROSSREFS
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See A035615 for a classic related base-2 sequence.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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