OFFSET
1,3
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). - Farideh Firoozbakht
LINKS
M. F. Hasler et al., Table of n, a(n) for n = 1..12
E. Angelini, Rang dans les Pairs/Impairs
E. Angelini, Rang dans les Pairs/Impairs [Cached copy, with permission]
E. Angelini et al., Rank of n in the Odd/Even sequence and follow-up messages on the SeqFan list, Feb 03 2009
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: seq(a(n), n=1..10); # Alois P. Heinz
MATHEMATICA
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 *)
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 */
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
EXTENSIONS
Typos fixed by Charles R Greathouse IV, Oct 28 2009
STATUS
approved