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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
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1,3
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COMMENTS
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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). - Farideh Firoozbakht
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LINKS
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MAPLE
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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: seq(a(n), n=1..10); # Alois P. Heinz
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=(v={}; Do[v= Join[v, IntegerDigits[a[k]]], {k, n-1}]; Floor[(1+FromDigits[v])/2]) (* Farideh Firoozbakht *)
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PROG
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(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
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Cf. A156146 (other starting values).
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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