A123522 Not of the form n + [log_10 n].

0, 10, 101, 1002, 10003, 100004, 1000005, 10000006, 100000007, 1000000008, 10000000009, 100000000010, 1000000000011, 10000000000012, 100000000000013, 1000000000000014, 10000000000000015, 100000000000000016

Offset: 0

Author

Ron R. King, Nov 10 2006

Keywords

• easy
• nonn

Comments

Smallest number such that (sum of digits) mod (number of digits) = n in decimal representation. - Reinhard Zumkeller, Aug 15 2010

Consider a word on the alphabet {0,1,2,...,9} that has length of 10^a(n). The expected number of occurrences of a pattern (contiguous subsequence) p_1,p_2,...p_n for all such words is 1. - Geoffrey Critzer, Feb 03 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 0..995
• Index entries for linear recurrences with constant coefficients, signature (12, -21, 10).

Programs

Magma

[10^n + n -1: n in [0..30]]; // G. C. Greubel, Nov 30 2017

Mathematica

Table[10^n + n - 1, {n, 0, 20}]  (* Geoffrey Critzer, Feb 03 2012 *)
LinearRecurrence[{12,-21,10},{0,10,101},20] (* Harvey P. Dale, Jul 20 2021 *)

PARI

for(n=0,30, print1(10^n + n -1, ", ")) \\ G. C. Greubel, Nov 30 2017

Formula

a(n) = 10^n + n - 1.

From Reinhard Zumkeller, Aug 15 2010: (Start)

A180160(a(n)) = n and A180160(m) <> n for m < a(n).

A007953(a(n)) = n; A055642(a(n)) = n + 1. (End)

From R. J. Mathar, Aug 15 2010: (Start)

G.f.: x*(-10+19*x) / ( (10*x-1)*(x-1)^2 ).

a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). (End)

Extensions

a(0) and terms beyond a(9) from Reinhard Zumkeller, Aug 15 2010