A240919 Sequence whose n-th term is the sum of the first n digits in the concatenation of the base 10-representation of the sequence.

9, 10, 10, 11, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 27, 28, 33, 34, 40, 41, 49, 50, 59, 61, 63, 65, 68, 70, 77, 79, 87, 90, 93, 96, 100, 104, 104, 108, 109, 113, 122, 127, 127, 132, 141, 147, 148, 154, 157, 163

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

Cf. A004207, A016096, A061939, A065075, A107975.

Sequence in context: A010735 A063543 A096166 * A078548 A095777 A168099

Adjacent sequences: A240916 A240917 A240918 * A240920 A240921 A240922

Keyword

nonn,base,easy

Author

Anthony Zajac, Aug 02 2014

Status

approved