1,3

Originally, round( c/2 ) was formulated as "rank of c in the sequence of odd resp. even (positive) numbers". Each of the rows has some characteristics reminiscent of Thue-Morse type sequences.

It's interesting that the number of digits of T(1,k) for k>2 equals to 2^(k-3). And for i>1 & k>1 [and i<20 - M.H.] the number of digits of T(i,k) equals to 2^(k-2). - F. Firoozbakht

A. P. Heinz, Table of n, a(n) for n=1,...,78

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

T(2,2)=1 since T(2,1)=2 is the 1st even number. T(2,3)=11 since concat(T(2,1),T(2,2))=21 is the 11-th odd number.

rank:= n-> `if` (irem(n, 2)=0, n/2, (n+1)/2); a:= proc (n, k) option remember; if n=1 then k else rank (parse (cat(seq(a(j, k), j=1..n-1)))) fi end; seq (seq (a(d-k, k), k=1..d-1), d=1..10); # Alois P. Heinz

A156146=concat( vector( 12, d, vector( d, k, T(k, d-k+1)))) /* M. F. Hasler */

Si[1]=i; Si[n_]:=Si[n]=(v={}; Do[v= Join[v, IntegerDigits[Si[k]]], {k, n-1}]; Floor[(1+FromDigits[v])/2]) (* F. Firoozbakht *)

(PARI) T(m, n)={ local(t=round(m/2)); n>1 | return(m); while( n-->1, t=round(1/2*m=eval(Str(m, t)))); t }

Cf. A156147 (first row of the table).

Sequence in context: A122761 A100469 A124320 this_sequence A154584 A129677 A077761

Adjacent sequences: A156143 A156144 A156145 this_sequence A156147 A156148 A156149

base,easy,nonn,tabl,new

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