OFFSET
1,3
COMMENTS
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 is 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. F. Hasler] the number of digits of T(i,k) equals to 2^(k-2). - Farideh Firoozbakht
LINKS
Alois P. Heinz, Table of n, a(n) for n=1..78
Eric Angelini, Rang dans les Pairs/Impairs
Eric Angelini, Rang dans les Pairs/Impairs [Cached copy, with permission]
Eric Angelini et al., Rank of n in the Odd/Even sequence and follow-up messages on the SeqFan list, Feb 03 2009
EXAMPLE
T(2,2) = 1 since T(2,1) = 2 is the first even number. T(2,3) = 11 since concat(T(2,1),T(2,2)) = 21 is the 11th odd number.
Table begins:
1, 1, 6, 58, 5829, 58292915, ...
2, 1, 11, 1056, 10555528, 1055552805277764, ...
3, 2, 16, 1608, 16080804, 1608080408040402, ...
4, 2, 21, 2111, 21106056, 2110605560553028, ...
5, 3, 27, 2664, 26636332, 2663633213318166, ...
6, 3, 32, 3166, 31661583, 3166158315830792, ...
MAPLE
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
MATHEMATICA
Si[1]=i; Si[n_]:=Si[n]=(v={}; Do[v= Join[v, IntegerDigits[Si[k]]], {k, n-1}]; Floor[(1+FromDigits[v])/2]) (* Farideh Firoozbakht *)
PROG
(PARI) T(m, n)={ my(t=round(m/2)); n>1 || return(m); while( n-- > 1, t=round(1/2*m=eval(Str(m, t)))); t }
A156146=concat( vector( 12, d, vector( d, k, T(k, d-k+1)))) /* M. F. Hasler */
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
Typos fixed by Charles R Greathouse IV, Oct 28 2009
STATUS
approved