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

1,2

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

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}]
nxt[{s_, a_}]:=With[{c=Max[IntegerDigits[s]]}, {c+s+2, c+2}]; NestList[nxt, {1, 1}, 100][[;; , 2]] (* Harvey P. Dale, Feb 12 2026 *)

Crossrefs

Sequence in context: A199951 A382243 A351101 * A151865 A124860 A182412

Adjacent sequences: A134545 A134546 A134547 * A134549 A134550 A134551

Keyword

base,nonn,look

Author

Zak Seidov, Oct 31 2007

Status

approved