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 A156146 Table T(m,n) = round( c(m,n)/2 ), where c(m,n) is the concatenation of all preceding terms in row m, T(m,1)...T(m,n-1) and T(m,1)=m. 4
 1, 1, 2, 6, 1, 3, 58, 11, 2, 4, 5829, 1056, 16, 2, 5, 58292915, 10555528, 1608, 21, 3, 6, 5829291479146458, 1055552805277764, 16080804, 2111, 27, 3, 7, 58292914791464577914645739573229, 10555528052777640527776402638882 (list; table; graph; refs; listen; history; text; internal format)
 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 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 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)={ local(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 Cf. A156147 (first row of the table). Sequence in context: A122761 A100469 A124320 * A192043 A154584 A129677 Adjacent sequences:  A156143 A156144 A156145 * A156147 A156148 A156149 KEYWORD base,easy,nonn,tabl AUTHOR Eric Angelini, Alois P. Heinz, Farideh Firoozbakht and M. F. Hasler, Feb 04 2009 EXTENSIONS Typos fixed by Charles R Greathouse IV, Oct 28 2009 STATUS approved

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)