OFFSET
1,1
COMMENTS
This is the unique sequence in base 10 with this property, aside from the trivial case of beginning this sequence with a(k)=0 for the first k terms.
The only possible nonzero values for a(1) and a(2) are 9 and 10, respectively. This is because a(1) must be a 1-digit number, while a(2) must equal the sum of its own first digit and a(1).
Likewise, for the analogous sequence in a different base b, the first two terms must be b-1 and b.
Essentially the same as A107975. - R. J. Mathar, Jul 07 2023
LINKS
Anthony Zajac, Table of n, a(n) for n = 1..10000
EXAMPLE
a(5) is the sum of the first 5 digits of "91010111112..." = 9 + 1 + 0 + 1 + 0 = 11.
MATHEMATICA
a240919 = {};
Do[
Which[Length[a240919] <= 0, AppendTo[a240919, 9],
Length[a240919] == 1,
AppendTo[a240919,
First[First[a240919] +
IntegerDigits[First[Plus[a240919, a240919]]]]],
True, AppendTo[a240919,
Total[Take[Flatten[Map[IntegerDigits, a240919]], n]]]], {n,
10000}]; TableForm[
Transpose[
List[Range[Length[a240919]],
a240919]]] (* Michael De Vlieger, Aug 05 2014 *)
PROG
(PARI) lista(nn) = {v = vector(nn); v[1] = 9; v[2] = 10; vd = [9, 1, 0]; print1(v[1], ", ", v[2], ", "); for (n=3, nn, v[n] = sum(k=1, n, vd[k]); vd = concat(vd, digits(v[n])); print1(v[n], ", "); ); } \\ Michel Marcus, Aug 14 2014
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Anthony Zajac, Aug 02 2014
STATUS
approved