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 A114965 #22 Jan 26 2025 09:12:48 %S A114965 34,35,38,43,50,59,70,83,98,115,134,155,178,203,230,259,290,323,358, %T A114965 395,434,475,518,563,610,659,710,763,818,875,934,995,1058,1123,1190, %U A114965 1259,1330,1403,1478,1555,1634,1715,1798,1883,1970,2059,2150,2243,2338,2435 %N A114965 a(n) = n^2 + 34. %C A114965 Conjecture: n^2 + 34 != x^k for all n,x and k > 1. %C A114965 The conjecture is true: See Cohn. - _James Rayman_, Feb 14 2023 %H A114965 J. H. E. Cohn, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa65/aa6546.pdf">The diophantine equation x^2 + C = y^n</a>, Acta Arithmetica LXV.4 (1993). %H A114965 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A114965 From _Elmo R. Oliveira_, Jan 25 2025: (Start) %F A114965 G.f.: (34 - 67*x + 35*x^2)/(1 - x)^3. %F A114965 E.g.f.: (34 + x + x^2)*exp(x). %F A114965 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End) %t A114965 34+Range[50]^2 (* _Harvey P. Dale_, Jan 28 2011 *) %o A114965 (PARI) a(n)=n^2+34 %Y A114965 Cf. A114948, A114962, A114963, A114964, A241850. %K A114965 easy,nonn %O A114965 0,1 %A A114965 _Cino Hilliard_, Feb 21 2006 %E A114965 Edited by _Charles R Greathouse IV_, Aug 09 2010 %E A114965 a(0) = 34 prepended by _Elmo R. Oliveira_, Jan 26 2025