cp's OEIS Frontend

A332191 a(n) = 10^(2n+1) - 1 - 8*10^n.

%I A332191 #12 Feb 11 2020 08:30:08
%S A332191 1,919,99199,9991999,999919999,99999199999,9999991999999,
%T A332191 999999919999999,99999999199999999,9999999991999999999,
%U A332191 999999999919999999999,99999999999199999999999,9999999999991999999999999,999999999999919999999999999,99999999999999199999999999999,9999999999999991999999999999999
%N A332191 a(n) = 10^(2n+1) - 1 - 8*10^n.
%C A332191 See A183184 = {1, 5, 13, 43, 169, 181, ...} for the indices of primes.
%H A332191 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp919">Palindromic Wing Primes: (9)1(9)</a>, updated: June 25, 2017.
%H A332191 Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99199.htm">Factorization of 9999199...99</a>, updated Dec 11 2018.
%H A332191 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332191 a(n) = 9*A138148(n) + 10^n.
%F A332191 G.f.: (1 + 808*x - 1700*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332191 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332191 A332191 := n -> 10^(n*2+1)-1-8*10^n;
%t A332191 Array[ 10^(2 # + 1)-1-8*10^# &, 15, 0]
%o A332191 (PARI) apply( {A332191(n)=10^(n*2+1)-1-8*10^n}, [0..15])
%o A332191 (Python) def A332191(n): return 10**(n*2+1)-1-8*10^n
%Y A332191 Cf. (A077776-1)/2 = A183184: indices of primes.
%Y A332191 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332191 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332191 Cf. A332121 .. A332181 (variants with different repeated digit 2, ..., 8).
%Y A332191 Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%K A332191 nonn,base,easy
%O A332191 0,2
%A A332191 _M. F. Hasler_, Feb 08 2020