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Numbers such that the outer 2 digits are 9 and the inner digits are 5.
1

%I #9 Sep 04 2024 09:53:38

%S 959,9559,95559,955559,9555559,95555559,955555559,9555555559,

%T 95555555559,955555555559,9555555555559,95555555555559,

%U 955555555555559,9555555555555559,95555555555555559,955555555555555559

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

%C 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.

%H Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/9559iscomposite.msnw">Proof 955..559 is composite</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11, -10).

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

%o (PARI) g(n,r,m) = \\ repeat rrr.. surrounded by 2 m's

%o { for(x=1,n, y=m*10^(x+1)+m+r*10*(10^x-1)/9; print(x",") ) }

%K easy,nonn,base

%O 1,1

%A _Cino Hilliard_, Jul 16 2005