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

1,2

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).

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)

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

Crossrefs

Cf. A090287, A338366.

Sequence in context: A046807 A333423 A178836 * A263926 A114788 A085074

Adjacent sequences: A338709 A338710 A338711 * A338713 A338714 A338715

Keyword

nonn,base,easy

Author

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

Status

approved