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

Author

J. Lowell, Jan 25 2024

Keywords

• nonn
• easy
• base

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

Examples

			a(3) = 105 = 7*15.
		

Links

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

Crossrefs

Cf. A033940, A241217, A369613.

Programs

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 *)

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