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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

(list; graph; refs; listen; history; text; internal format)

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

URL: https://oeis.org/A266959

⇱ A266959 - OEIS