A338712 Numbers with all digits equal and from the set {1, 3, 7, 9}.

1, 3, 7, 9, 11, 33, 77, 99, 111, 333, 777, 999, 1111, 3333, 7777, 9999, 11111, 33333, 77777, 99999, 111111, 333333, 777777, 999999, 1111111, 3333333, 7777777, 9999999, 11111111, 33333333, 77777777, 99999999, 111111111, 333333333, 777777777, 999999999, 1111111111, 3333333333, 7777777777, 9999999999

Offset: 1

Author

N. J. A. Sloane, Nov 08 2020, following a suggestion from Hugo Pfoertner

Keywords

• nonn
• base
• easy
• changed

Comments

Candidates for prefixes and suffixes in A090287.

Links

• Robert Price, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,11,0,0,0,-10).

Crossrefs

Cf. A065444, A090287, A338366.

Programs

Maple

a:= n-> [1, 3, 7, 9][1+irem(n-1, 4)]*(10^iquo(n+3, 4)-1)/9:
seq(a(n), n=1..50);  # Alois P. Heinz, Nov 09 2020

Mathematica

A338712={}; Do[AppendTo[A338712, FromDigits[ConstantArray[#,i]] & /@{ 1,3,7,9}], {i,10}]; A338712//Flatten (* Robert Price, Sep 21 2023 *)

Formula

From Colin Barker, Nov 09 2020: (Start)

G.f.: x*(1 + 3*x + 7*x^2 + 9*x^3) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - 10*x^4)).

a(n) = 11*a(n-4) - 10*a(n-8) for n>8. (End)

Sum_{n>=1} 1/a(n) = (100/63) * A065444. - Amiram Eldar, Aug 31 2025