A134548 a(1)=1, a(n) = 2 + maximal digit of Sum_{j=1..n-1} a(j).

1, 3, 6, 3, 5, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 4, 6, 5, 7, 6, 10, 10, 10, 10, 10, 11, 11, 4, 6, 5, 7, 6, 10, 10, 10, 10, 10, 11, 11, 5, 7, 5, 9, 8, 7, 8, 11, 10, 11, 6, 9, 8, 6, 6, 8, 6, 7, 9, 8, 9, 10, 11, 7, 7, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 8, 10, 10, 10, 10, 10, 10, 10

Offset: 1

Author

Zak Seidov, Oct 31 2007

Keywords

• base
• nonn
• look

Comments

For n > 1, 3 <= a(n) <= 11 by definition. Also subsequences with repeating terms may be arbitrarily long. What about any other patterns, periods, etc.?

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Robert Israel, Plot of a(n) for n = 1 .. 5*10^5

Programs

Maple

s:= proc(n) option remember;
   procname(n-1) + a(n-1)
end proc:
s(1):= 0:
a:=  proc(n) 2 + max(convert(s(n),base,10)) end proc:
a(1):= 1:
map(a, [$1..100]); # Robert Israel, May 19 2025

Mathematica

a[1]=i=s=1;Do[i++;b=2+Max[IntegerDigits[s]];a[i]=b;s+=b,{145}]; Table[a[k],{k,i}]