cp's OEIS Frontend

A332114 a(n) = (10^(2n+1)-1)/9 + 3*10^n.

%I A332114 #8 Feb 11 2020 07:56:53
%S A332114 4,141,11411,1114111,111141111,11111411111,1111114111111,
%T A332114 111111141111111,11111111411111111,1111111114111111111,
%U A332114 111111111141111111111,11111111111411111111111,1111111111114111111111111,111111111111141111111111111,11111111111111411111111111111,1111111111111114111111111111111
%N A332114 a(n) = (10^(2n+1)-1)/9 + 3*10^n.
%C A332114 See A107124 = {2, 3, 32, 45, 1544, ...} for the indices of primes.
%H A332114 Brady Haran and Simon Pampena, <a href="https://youtu.be/HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%H A332114 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp141">Palindromic Wing Primes: (1)4(1)</a>, updated: June 25, 2017.
%H A332114 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11411.htm">Factorization of 11...11411...11</a>, updated Dec 11 2018.
%H A332114 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332114 a(n) = A138148(n) + 4*10^n = A002275(2n+1) + 3*10^n.
%F A332114 G.f.: (4 - 303*x + 200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332114 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332114 A332114 := n -> (10^(2*n+1)-1)/9+3*10^n;
%t A332114 Array[(10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
%o A332114 (PARI) apply( {A332114(n)=10^(n*2+1)\9+3*10^n}, [0..15])
%o A332114 (Python) def A332114(n): return 10**(n*2+1)//9+3*10**n
%Y A332114 Cf. (A077780-1)/2 = A107124: indices of primes; A331866 & A331867 (non-palindromic variants).
%Y A332114 Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
%Y A332114 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332114 Cf. A332124 .. A332194 (variants with different repeated digit 2, ..., 9).
%Y A332114 Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
%K A332114 nonn,base,easy
%O A332114 0,1
%A A332114 _M. F. Hasler_, Feb 09 2020