This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002277 #87 Jul 21 2025 00:25:55
%S A002277 0,3,33,333,3333,33333,333333,3333333,33333333,333333333,3333333333,
%T A002277 33333333333,333333333333,3333333333333,33333333333333,
%U A002277 333333333333333,3333333333333333,33333333333333333,333333333333333333,3333333333333333333,33333333333333333333,333333333333333333333
%N A002277 a(n) = 3*(10^n - 1)/9.
%C A002277 From _Wolfdieter Lang_, Feb 08 2017: (Start)
%C A002277 This sequence (for n >= 1) appears in n-families satisfying so-called curious cubic identities based on the Armstrong numbers 153, 370 and 371, A005188(10) - A005188(12).
%C A002277 153 also involves A246057(n-1) and A093143(n). See a comment in A246057 with the van Poorten et al. reference, and A281857.
%C A002277 370 and 371 also involve A067275(n+1). See the comment there, and A281858 and A281860. (End)
%H A002277 Ivan Panchenko, <a href="/A002277/b002277.txt">Table of n, a(n) for n = 0..200</a>
%H A002277 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repdigit.html">Repdigit</a>.
%H A002277 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A002277 a(n) = 3*A002275(n).
%F A002277 a(n) = A178631(n)/A002283(n). - _Reinhard Zumkeller_, May 31 2010
%F A002277 From _Vincenzo Librandi_, Jul 22 2010: (Start)
%F A002277 a(n) = a(n-1) + 3*10^(n-1) with a(0)=0;
%F A002277 a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=3. (End)
%F A002277 G.f.: 3*x/((1 - x)*(1 - 10*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F A002277 Sum_{n>=1} 1/a(n) = A135702. - _Amiram Eldar_, Nov 13 2020
%F A002277 E.g.f.: exp(x)*(exp(9*x) - 1)/3. - _Stefano Spezia_, Sep 13 2023
%F A002277 From _Elmo R. Oliveira_, Jul 20 2025: (Start)
%F A002277 a(n) = (A246057(n) - 1)/5.
%F A002277 a(n) = A010785(A017197(n-1)) for n >= 1. (End)
%e A002277 From _Wolfdieter Lang_, Feb 08 2017: (Start)
%e A002277 Curious cubic identities (see a comment above):
%e A002277 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ...
%e A002277 3^3 + 7^3 + 0^3 = 370; 336700 = 33^3 + 67^3 + (00)^3 = 336700, 333^3 + 667^3 + (000)^3 = 333667000, ...
%e A002277 3^3 + 7^3 + 1^3 = 371, 33^3 + 67^3 + (01)^3 = 336701, 333^3 + 667^3 + (001)^3 = 333667001, ... (End)
%p A002277 A002277:=n->(10^n-1)/3: seq(A002277(n), n=0..30); # _Wesley Ivan Hurt_, Apr 01 2016
%t A002277 LinearRecurrence[{11, -10}, {0, 3}, 20] (* _Robert G. Wilson v_, Jul 06 2013 *)
%t A002277 (10^Range[0, 30] - 1)/3 (* _Wesley Ivan Hurt_, Apr 01 2016 *)
%o A002277 (Maxima) A002277(n):=(10^n - 1)/3$
%o A002277 makelist(A002277(n),n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%o A002277 (PARI) a(n)=(10^n-1)/3 \\ _Charles R Greathouse IV_, Sep 24 2015
%o A002277 (Magma) [(10^n - 1)/3 : n in [0..30]]; // _Wesley Ivan Hurt_, Apr 01 2016
%Y A002277 Cf. A002275, A002276, A002278, A002279, A002280, A002281, A002282, A002283, A010785, A017197.
%Y A002277 Cf. A005188, A067275, A075412, A093143, A135702, A178631, A178633, A246057, A281857, A281858, A281860.
%K A002277 easy,nonn
%O A002277 0,2
%A A002277 _N. J. A. Sloane_