A078998 Choose a(n) so that a(1)+a(2)+...+a(n) = concatenation of n first natural numbers.

1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 12222222121, 1222222212101, 122222221210101, 12222222121010101, 1222222212101010101, 122222221210101010101, 12222222121010101010101

Offset: 1

Author

Benoit Cloitre, Jan 12 2003

Keywords

• nonn
• base

Crossrefs

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793.

Programs

Mathematica

b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; AppendTo[b, p], {n, 1, 30}]; c = {}; Do[AppendTo[c, b[[n + 1]] - b[[n]]], {n, 1, Length[b] - 1}]; c (* Artur Jasinski, Mar 30 2008 *)

Formula

a(1)=1; for n>1, a(n) = A007908(n)-A007908(n-1)