A332195 - OEIS

%I #12 Feb 11 2020 08:32:34

%S 5,959,99599,9995999,999959999,99999599999,9999995999999,

%T 999999959999999,99999999599999999,9999999995999999999,

%U 999999999959999999999,99999999999599999999999,9999999999995999999999999,999999999999959999999999999,99999999999999599999999999999,9999999999999995999999999999999

%N a(n) = 10^(2n+1) - 4*10^n - 1.

%C See A183186 = {88, 112, 198, 622, 4228, ...} for the indices of primes.

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp959">Palindromic Wing Primes: (9)5(9)</a>, updated Jun 25 2017.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99599.htm">Factorization of 99...99599...99</a>, updated Dec 11 2018.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F a(n) = 9*A138148(n) + 5*10^n.

%F G.f.: (5 + 404*x - 1300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

%p A332195 := n -> 10^(n*2+1)-4*10^n-1;

%t Array[ 10^(2 # + 1) - 1 - 4*10^# &, 15, 0]

%o (PARI) apply( {A332195(n)=10^(n*2+1)-1-4*10^n}, [0..15])

%o (Python) def A332195(n): return 10**(n*2+1)-1-4*10^n

%Y Cf. (A077786-1)/2 = A183186: indices of primes.

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).

%Y Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).

%Y Cf. A332115 .. A332185 (variants with different repeated digit 1, ..., 8).

%Y Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 08 2020