A318919 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].

1, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..64.

Example

The initial values of b(0), b(1), ... are:
b(0) = 0
b(1) = [1, 1]
b(2) = [2, 3]
b(3) = [2, 5]
b(4) = [2, 7]
b(5) = [2, 9]
b(6) = [2, 11]
b(7) = [3, 14]
b(8) = [3, 17]
b(9) = [3, 20]
b(10) = [3, 23]
b(11) = [3, 26]
b(12) = [3, 29]
...
The second terms give the present sequence.
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).

Maple

A055642 := proc(n) max(1, ilog10(n)+1) ; end proc:
read transforms;
M:=1000;
b[1]:=[1, 1];
for n from 2 to M do
b[n][1]:=A055642(b[n-1][1]) + A055642(b[n-1][2]);
b[n][2]:=b[n-1][2]+b[n][1];
od:
s2:=[seq(b[n][2], n=1..M)]; # A318919
s1:=[seq(b[n][1], n=1..M)]: RUNS(s1); # A318920

Crossrefs

For b(n)[1] see A318920.

Sequence in context: A066665 A278451 A175269 * A279539 A174059 A321676

Adjacent sequences: A318916 A318917 A318918 * A318920 A318921 A318922

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 06 2018

Status

approved