1,3

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

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

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

(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 *)

(PARI) A156147(n)={local(a=1, t=1); while(n-->1, t=round(1/2*a=eval(Str(a, t)))); t} /* M. F. Hasler */

Cf. A156146 (other starting values).

Sequence in context: A073848 A141382 A034982 this_sequence A024269 A114501 A089153

Adjacent sequences: A156144 A156145 A156146 this_sequence A156148 A156149 A156150

base,easy,nonn

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 (MHasler(AT)univ-ag.fr), Feb 04 2009

Typos fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009