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A156147 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.

%I A156147 #30 Dec 23 2024 14:53:42
%S A156147 1,1,6,58,5829,58292915,5829291479146458,
%T A156147 58292914791464577914645739573229,
%U A156147 5829291479146457791464573957322929146457395732288957322869786615
%N A156147 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.
%C A156147 Originally, round( c/2 ) was formulated as "rank of c in the sequence of odd resp. even (positive) numbers".
%C A156147 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_
%C A156147 It's interesting that the number of digits of a(k) for k>2 equals to 2^(k-3). - _Farideh Firoozbakht_
%H A156147 M. F. Hasler et al., <a href="/A156147/b156147.txt">Table of n, a(n) for n = 1..12</a>
%H A156147 E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ThueMorseRank.htm">Rang dans les Pairs/Impairs</a>
%H A156147 E. Angelini, <a href="/A156146/a156146.pdf">Rang dans les Pairs/Impairs</a> [Cached copy, with permission]
%H A156147 E. Angelini et al., <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2009-February/000740.html">Rank of n in the Odd/Even sequence</a> and follow-up messages on the SeqFan list, Feb 03 2009
%p A156147 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_
%t A156147 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_ *)
%o A156147 (PARI) A156147(n)={local(a=1,t=1); while(n-->1,t=round(1/2*a=eval(Str(a,t))));t} /* _M. F. Hasler_ */
%Y A156147 Cf. A156146 (other starting values).
%K A156147 base,easy,nonn
%O A156147 1,3
%A A156147 _Eric Angelini_, _Alois P. Heinz_, _Farideh Firoozbakht_ and _M. F. Hasler_, Feb 04 2009
%E A156147 Typos fixed by _Charles R Greathouse IV_, Oct 28 2009