A108903 Numbers such that the outer 2 digits are 9 and the inner digits are 5.

959, 9559, 95559, 955559, 9555559, 95555559, 955555559, 9555555559, 95555555559, 955555555559, 9555555555559, 95555555555559, 955555555555559, 9555555555555559, 95555555555555559, 955555555555555559

Offset: 1

Author

Cino Hilliard, Jul 16 2005

Keywords

• easy
• nonn
• base

Comments

These numbers are all composite. They are divisible among other numbers by 3,7,11,13 depending on the form 6k+r, 0 < r < 6. See the link for a proof.

Links

• Cino Hilliard, Proof 955..559 is composite.
• Index entries for linear recurrences with constant coefficients, signature (11, -10).

Programs

PARI

g(n,r,m) = \\ repeat rrr.. surrounded by 2 m's
{ for(x=1,n, y=m*10^(x+1)+m+r*10*(10^x-1)/9; print(x",") ) }

Formula

S(x)=9*10^(x+1)+ 9 + 50*(10^x-1)/9.