A266959 Smallest n-digit number ending in n.

1, 12, 103, 1004, 10005, 100006, 1000007, 10000008, 100000009, 1000000010, 10000000011, 100000000012, 1000000000013, 10000000000014, 100000000000015, 1000000000000016, 10000000000000017, 100000000000000018, 1000000000000000019, 10000000000000000020

Offset

1,2

Comments

Digital sum of a(n) = digsum(n) + 1 for n>1.

3, 229, 4987 are the initial values of n for prime a(n). - Altug Alkan, Jan 17 2016

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Formula

a(n) = n + 10^(n-1) for n>1 with a(1) = 1.

a(n) = A081552(n) - 1 for n>1. - Michel Marcus, Jan 10 2016

From Colin Barker, Jan 10 2016: (Start)

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

G.f.: x*(1-20*x^2+10*x^3) / ((1-x)^2*(1-10*x)). (End)

Example

a(4) = 1004 because it is the smallest 4-digit number ending in 4.

Maple

A266959:=n->n+10^(n-1): 1, seq(A266959(n), n=2..30);

Mathematica

Join[{1}, Table[n + 10^(n - 1), {n, 2, 20}]]

Prog

(Magma) [1] cat [n+10^(n-1): n in [2..30]]; // Vincenzo Librandi, Jan 10 2016
(PARI) Vec(x*(1-20*x^2+10*x^3)/((1-x)^2*(1-10*x)) + O(x^30)) \\ Colin Barker, Jan 10 2016
(PARI) a(n) = if(n==1, 1, n + 10^(n-1)); \\ Altug Alkan, Jan 17 2016
(Python)
def A266959(n): return n+10**(n-1) if n > 1 else 1 # Chai Wah Wu, Jul 25 2022

Crossrefs

Cf. A007953 (digsum), A081552, A279913.

Sequence in context: A264452 A078397 A228988 * A262778 A099293 A024454

Adjacent sequences: A266956 A266957 A266958 * A266960 A266961 A266962

Keyword

nonn,easy,base

Author

Wesley Ivan Hurt, Jan 09 2016

Status

approved