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

1,1

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

Table of n, a(n) for n=1..18.

Cino Hilliard, Proof 94..49

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

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A108903, A108904.

Sequence in context: A020366 A217936 A013532 * A260174 A285157 A096954

Adjacent sequences: A108893 A108894 A108895 * A108897 A108898 A108899

Keyword

easy,nonn,base

Author

Cino Hilliard, Jul 16 2005

Status

approved