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A156147
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a(n+1) = round( c(n)/2 ), where c(n) is the concatenation of all preceding terms a(1)...a(n) and a(1)=1.
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4
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OFFSET
| 1,3
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COMMENTS
| Originally, round( c/2 ) was formulated as "rank of c in the sequence of odd resp. even (positive) numbers".
The sequence has some characteristics reminiscent of Thue-Morse type sequences. It "converges" to a non-periodic sequence of digits: all but the last digit of a given term will remain the initial digits of all subsequent terms. - M. F. Hasler
It's interesting that the number of digits of a(k) for k>2 equals to 2^(k-3). - F. Firoozbakht
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LINKS
| M. F. Hasler et al., Table of n, a(n) for n=1,...,12
E. Angelini, Rang dans les Pairs/Impairs
E. Angelini et al., Rank of n in the Odd/Even sequence and follow-up messages on the SeqFan list, Feb 03 2009
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MAPLE
| rank:= n-> `if` (irem(n, 2)=0, n/2, (n+1)/2); a:= proc (n) option remember; if n=1 then 1 else rank (parse (cat(seq(a(j), j=1..n-1)))) fi end; # Alois P. Heinz
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MATHEMATICA
| (Mathematica) Si[1]=1; Si[n_]:=Si[n]=(v={}; Do[v= Join[v, IntegerDigits[Si[k]]], {k, n-1}]; Floor[(1+FromDigits[v])/2]) (* F. Firoozbakht *)
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PROG
| (PARI) A156147(n)={local(a=1, t=1); while(n-->1, t=round(1/2*a=eval(Str(a, t)))); t} /* M. F. Hasler */
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CROSSREFS
| Cf. A156146 (other starting values).
Sequence in context: A073848 A141382 A034982 * A024269 A114501 A089153
Adjacent sequences: A156144 A156145 A156146 * A156148 A156149 A156150
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KEYWORD
| base,easy,nonn
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AUTHOR
| E. Angelini (eric.angelini(AT)kntv.be), A. P. Heinz (heinz(AT)hs-heilbronn.de), F. Firoozbakht (mymontain(AT)yahoo.com) and M. F. Hasler (www.univ-ag.fr/~mhasler), Feb 04 2009
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EXTENSIONS
| Typos fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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