A108896 Numbers whose outer two digits are 9's and inner digits are 4's.

949, 9449, 94449, 944449, 9444449, 94444449, 944444449, 9444444449, 94444444449, 944444444449, 9444444444449, 94444444444449, 944444444444449, 9444444444444449, 94444444444444449, 944444444444444449, 9444444444444444449, 94444444444444444449

Offset: 1

Author

Cino Hilliard, Jul 16 2005

Keywords

• easy
• nonn
• base

Comments

All terms are composite.

From Sergio Pimentel, Jul 26 2022: (Start)

a(n) is divisible by:

13 if n == 1 (mod 6).

11 if n == 0,2,4 (mod 6).

3 if n == 0,3 (mod 6).

7 if n == 5 (mod 6). (End)

Links

• Cino Hilliard, Proof 94..49
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A108903, A108904.

Programs

Mathematica

Table[10*FromDigits[PadRight[{9},n,4]]+9,{n,2,20}] (* Harvey P. Dale, Apr 02 2018 *)

PARI

S(n,r,m)=for(x=1,n,y=m*10^(x+1)+m+r*10*(10^x-1)/9;print1(y","))

Python

def a(n): return int('9' + '4'*n + '9')
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jul 26 2022

Formula

a(n) = 9*10^(n+1) + 9 + 40*(10^n-1)/9.

From Chai Wah Wu, Jul 27 2022: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.

G.f.: x*(949 - 990*x)/((x - 1)*(10*x - 1)). (End)