A369562 Smallest positive n-digit number divisible by 7.

7, 14, 105, 1001, 10003, 100002, 1000006, 10000004, 100000005, 1000000001, 10000000003, 100000000002, 1000000000006, 10000000000004, 100000000000005, 1000000000000001, 10000000000000003, 100000000000000002, 1000000000000000006, 10000000000000000004, 100000000000000000005

Offset

1,1

Comments

The only semiprime terms are a(2) = 14 and a(n) such that (10^(n-1) + 3)/7 is a prime. - Jon E. Schoenfield, Jan 27 2024

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1,11,-10).

Formula

a(n) = (floor(10^(n-1)/7) + 1)*7.

a(n) = 10^(n-1) + A033940(n+2). - Amiram Eldar, Jan 27 2024

G.f.: 7*x*(1 - 9*x + 3*x^2 - x^3 - 3*x^4)/((1 - x)*(1 + x)*(1 - 10*x)*(1 - x + x^2)). - Stefano Spezia, Jan 28 2024

Example

a(3) = 105 = 7*15.

Mathematica

a[n_] := 10^(n - 1) + {6, 4, 5, 1, 3, 2}[[Mod[n, 6, 1]]]; Array[a, 30]
(* or *)
LinearRecurrence[{11, -10, -1, 11, -10}, {7, 14, 105, 1001, 10003, 100002}, 30] (* Amiram Eldar, Jan 27 2024 *)
Table[10^n+7-PowerMod[10, n, 7], {n, 0, 20}] (* Harvey P. Dale, Jan 13 2025 *)

Crossrefs

Cf. A033940, A241217, A369613.

Sequence in context: A196254 A173167 A143682 * A080451 A346534 A369122

Adjacent sequences: A369559 A369560 A369561 * A369563 A369564 A369565

Keyword

nonn,easy,base

Author

J. Lowell, Jan 25 2024

Status

approved