%I #13 Aug 23 2024 08:40:53
%S 1,2,6,13,7,4,37,19,10,955,478,477739,238870,238869619435,
%T 119434809718,119434809717559717404859,59717404858779858702430,
%U 5971740485877985870242979858702429389929351215
%N Start with 1 and 2; if number is even concatenate with last number and divide by 2, if it is odd add 1 and divide by 2.
%C Rapidly growing: for n=10,20,30,40,50 the terms have 3, 138, 914, 3649, 248128 digits respectively (cf. A131059). - _Hieronymus Fischer_, Jun 12 2007
%F a(n) = ceiling(a(n-1)/2)+(1+(-1)^a(n-1))*10^floor(log_10(a(n-1))+1)*a(n-2)/4, n>=2. - _Hieronymus Fischer_, Jun 12 2007
%e a(1) = 2 is even, so concatenate a(0) and a(1), divide by 2: a(2) = 12/2 = 6.
%e a(2) = 6 is even, so concatenate a(1) and a(2), divide by 2: a(3) = 26/2 = 13.
%e a(3) = 13 is odd, so add 1, divide by 2: a(4) = 14/2 = 7.
%t a[0]=1;a[1]=2;a[n_]:=If[EvenQ[a[n-1]],FromDigits[Join[IntegerDigits[a[n-2]],IntegerDigits[a[n-1]]]]/2,(a[n-1]+1)/2];Table[a[n],{n,0,17}] (* _James C. McMahon_, Aug 22 2024 *)
%Y Cf. A131059.
%K nonn,base
%O 0,2
%A _Rodolfo Kurchan_, Mar 26 2006
%E More terms from _Hieronymus Fischer_, Jun 12 2007