A318919 - OEIS

%I #16 Sep 06 2018 17:26:09

%S 1,3,5,7,9,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,65,

%T 68,71,74,77,80,83,86,89,92,95,98,101,105,109,113,117,121,125,129,133,

%U 137,141,145,149,153,157,161,165,169,173,177,181,185,189,193,197,201,205,209,213

%N Define b(0)=0, b(1)[1]=1, b(1)[2]=1; and for n>=2, b(n)[1] = total number of digits in b(n-1), and b(n)[2] = total number of digits in b(0),...,b(n-1); a(n) = b(n)[2].

%D Eric Angelini, Posting to Math Fun Mailing List, Aug 20 2007.

%e The initial values of b(0), b(1), ... are:

%e b(0) = 0

%e b(1) = [1, 1]

%e b(2) = [2, 3]

%e b(3) = [2, 5]

%e b(4) = [2, 7]

%e b(5) = [2, 9]

%e b(6) = [2, 11]

%e b(7) = [3, 14]

%e b(8) = [3, 17]

%e b(9) = [3, 20]

%e b(10) = [3, 23]

%e b(11) = [3, 26]

%e b(12) = [3, 29]

%e ...

%e The second terms give the present sequence.

%e The sequence of values of the first terms b(i)[1] for i >= 1 consists of 1 (once), 2 (5 times), 3 (30 times), 4 (225 times), 5 (1800 times), 6 (15000 times), ... (see A318920).

%p A055642 := proc(n) max(1, ilog10(n)+1) ; end proc:

%p read transforms;

%p M:=1000;

%p b[1]:=[1,1];

%p for n from 2 to M do

%p b[n][1]:=A055642(b[n-1][1]) + A055642(b[n-1][2]);

%p b[n][2]:=b[n-1][2]+b[n][1];

%p od:

%p s2:=[seq(b[n][2],n=1..M)]; # A318919

%p s1:=[seq(b[n][1],n=1..M)]: RUNS(s1); # A318920

%Y For b(n)[1] see A318920.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Sep 06 2018