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

Author

Anthony Zajac, Aug 02 2014

Keywords

• nonn
• base
• easy

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

Examples

			a(5) is the sum of the first 5 digits of "91010111112..." = 9 + 1 + 0 + 1 + 0 = 11.
		

Links

• Anthony Zajac, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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 *)

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