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 A070875 #67 Dec 30 2024 02:23:08
%S A070875 5,7,10,14,20,28,40,56,80,112,160,224,320,448,640,896,1280,1792,2560,
%T A070875 3584,5120,7168,10240,14336,20480,28672,40960,57344,81920,114688,
%U A070875 163840,229376,327680,458752,655360,917504,1310720,1835008,2621440
%N A070875 Binary expansion is 1x100...0 where x = 0 or 1.
%C A070875 A 2-automatic sequence. - _Charles R Greathouse IV_, Sep 24 2012
%C A070875 Third row in array A228405. - _Richard R. Forberg_, Sep 06 2013
%C A070875 Conjecture: a(n) = -1 + positions of the ones in A309019(n+2) - A002487(n+2). - _George Beck_, Mar 26 2022
%C A070875 Consecutive integers for which the number of its proper nondivisors of the form 2^k (k > 0) is 2; proper nondivisors are defined in A173540 (5 has two such nondivisors: 2 and 4, 7 has 2 and 4, 10 has 4 and 8, 14 has 4 and 8, 20 has 8 and 16,...). - _Lechoslaw Ratajczak_, Dec 17 2024
%H A070875 Vincenzo Librandi, <a href="/A070875/b070875.txt">Table of n, a(n) for n = 0..1000</a>
%H A070875 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%H A070875 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A070875 A093873(a(n)) = 2. - _Reinhard Zumkeller_, Oct 13 2006
%F A070875 For n>1, a(n+1) = a(n) + A000010(a(n)). - _Stefan Steinerberger_, Dec 20 2007
%F A070875 From _Bruno Berselli_, Mar 01 2011: (Start)
%F A070875 G.f.: (5+7*x)/(1-2*x^2).
%F A070875 a(n) = (6-(-1)^n)*2^((2*n+(-1)^n-1)/4). Therefore: a(n) = 5*2^(n/2) for n even, otherwise a(n) = 7*2^((n-1)/2).
%F A070875 a(n) = 2*a(n-2) for n>1. (End)
%F A070875 a(n+1) = A063757(n) + 6. - _Philippe Deléham_, Apr 13 2013
%F A070875 a(n) = sqrt(2*a(n-1) - (-2)^(n-1)). - _Richard R. Forberg_, Sep 06 2013
%F A070875 a(n+3) = a(n+2)*a(n+1)/a(n). - _Richard R. Forberg_, Sep 06 2013
%F A070875 For n>1, a(n) = 2*phi(a(n)) + phi(phi(a(n))). - _Ivan Neretin_, Feb 28 2016
%F A070875 a(2n) = A020714(n), a(2n+1) = A005009(n); for n>0. - _Yosu Yurramendi_, Jun 01 2016
%F A070875 From _Ilya Gutkovskiy_, Jun 02 2016: (Start)
%F A070875 E.g.f.: 7*sinh(sqrt(2)*x)/sqrt(2) + 5*cosh(sqrt(2)*x).
%F A070875 a(n) = 2^((n-3)/2)*(5*sqrt(2)*(1 + (-1)^n) + 7*(1 - (-1)^n)). (End)
%F A070875 Sum_{n>=0} 1/a(n) = 24/35. - _Amiram Eldar_, Mar 28 2022
%t A070875 Flatten@ NestList[ 2# &, {5, 7}, 19] (* Or *)
%t A070875 CoefficientList[ Series[(5 + 7 x)/(1 - 2 x^2), {x, 0, 38}], x] (* _Robert G. Wilson v_, May 20 2002 *)
%o A070875 (Magma) [n le 2 select 2*n+3 else 2*Self(n-2): n in [1..39]]; // _Bruno Berselli_, Mar 01 2011
%o A070875 (PARI) a(n)=if(n%2,7,5)<<(n\2) \\ _Charles R Greathouse IV_, Sep 24 2012
%Y A070875 Cf. A070876, A123760, A063920.
%K A070875 nonn,base,easy
%O A070875 0,1
%A A070875 _N. J. A. Sloane_, May 19 2002
%E A070875 Extended by _Robert G. Wilson v_, May 20 2002