

A240919


The sequence whose nth term is the sum of the first n digits in the concatenation of the base 10 representation of the sequence.


1



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
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OFFSET

1,1


COMMENTS

This is the unique sequence in base 10 with this property, aside from the trivial case of beginning this series 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 1digit 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 b1 and b.


LINKS

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


EXAMPLE

a(5) = 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.
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



