A070875 Binary expansion is 1x100...0 where x = 0 or 1.

5, 7, 10, 14, 20, 28, 40, 56, 80, 112, 160, 224, 320, 448, 640, 896, 1280, 1792, 2560, 3584, 5120, 7168, 10240, 14336, 20480, 28672, 40960, 57344, 81920, 114688, 163840, 229376, 327680, 458752, 655360, 917504, 1310720, 1835008, 2621440

Offset: 0

Author

N. J. A. Sloane, May 19 2002

Keywords

• nonn
• base
• easy

Comments

A 2-automatic sequence. - Charles R Greathouse IV, Sep 24 2012

Third row in array A228405. - Richard R. Forberg, Sep 06 2013

Conjecture: a(n) = -1 + positions of the ones in A309019(n+2) - A002487(n+2). - George Beck, Mar 26 2022

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2).
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A070876, A123760, A063920.

Programs

Magma

[n le 2 select 2*n+3 else 2*Self(n-2): n in [1..39]]; // Bruno Berselli, Mar 01 2011

Mathematica

Flatten@ NestList[ 2# &, {5, 7}, 19] (* Or *)
CoefficientList[ Series[(5 + 7 x)/(1 - 2 x^2), {x, 0, 38}], x] (* Robert G. Wilson v, May 20 2002 *)

PARI

a(n)=if(n%2,7,5)<<(n\2) \\ Charles R Greathouse IV, Sep 24 2012

Formula

A093873(a(n)) = 2. - Reinhard Zumkeller, Oct 13 2006

For n>1, a(n+1) = a(n) + A000010(a(n)). - Stefan Steinerberger, Dec 20 2007

From Bruno Berselli, Mar 01 2011: (Start)

G.f.: (5+7*x)/(1-2*x^2).

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).

a(n) = 2*a(n-2) for n>1. (End)

a(n+1) = A063757(n) + 6. - Philippe Deléham, Apr 13 2013

a(n) = sqrt(2*a(n-1) - (-2)^(n-1)). - Richard R. Forberg, Sep 06 2013

a(n+3) = a(n+2)*a(n+1)/a(n). - Richard R. Forberg, Sep 06 2013

For n>1, a(n) = 2*phi(a(n)) + phi(phi(a(n))). - Ivan Neretin, Feb 28 2016

a(2n) = A020714(n), a(2n+1) = A005009(n); for n>0. - Yosu Yurramendi, Jun 01 2016

From Ilya Gutkovskiy, Jun 02 2016: (Start)

E.g.f.: 7*sinh(sqrt(2)*x)/sqrt(2) + 5*cosh(sqrt(2)*x).

a(n) = 2^((n-3)/2)*(5*sqrt(2)*(1 + (-1)^n) + 7*(1 - (-1)^n)). (End)

Sum_{n>=0} 1/a(n) = 24/35. - Amiram Eldar, Mar 28 2022

Extensions

Extended by Robert G. Wilson v, May 20 2002