cp's OEIS Frontend

A332115 a(n) = (10^(2n+1)-1)/9 + 4*10^n.

%I A332115 #8 Feb 11 2020 07:57:15
%S A332115 5,151,11511,1115111,111151111,11111511111,1111115111111,
%T A332115 111111151111111,11111111511111111,1111111115111111111,
%U A332115 111111111151111111111,11111111111511111111111,1111111111115111111111111,111111111111151111111111111,11111111111111511111111111111,1111111111111115111111111111111
%N A332115 a(n) = (10^(2n+1)-1)/9 + 4*10^n.
%C A332115 See A107125 = {0, 1, 7, 45, 115, 681, 1248, ...} for the indices of primes.
%H A332115 Brady Haran and Simon Pampena, <a href="https://youtu.be/HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%H A332115 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp151">Palindromic Wing Primes: (1)5(1)</a>, updated: June 25, 2017.
%H A332115 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11511.htm">Factorization of 11...11511...11</a>, updated Dec 11 2018.
%H A332115 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332115 a(n) = A138148(n) + 5*10^n = A002275(2n+1) + 4*10^n.
%F A332115 G.f.: (5 - 404*x + 300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332115 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332115 A332115 := n -> (10^(2*n+1)-1)/9+4*10^n;
%t A332115 Array[(10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
%o A332115 (PARI) apply( {A332115(n)=10^(n*2+1)\9+4*10^n}, [0..15])
%o A332115 (Python) def A332115(n): return 10**(n*2+1)//9+4*10**n
%Y A332115 Cf. (A077783-1)/2 = A107125: indices of primes; A331868 & A331869 (non-palindromic variants).
%Y A332115 Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
%Y A332115 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332115 Cf. A332125 .. A332195 (variants with different repeated digit 2, ..., 9).
%Y A332115 Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
%K A332115 nonn,base,easy
%O A332115 0,1
%A A332115 _M. F. Hasler_, Feb 09 2020