A083575 a(0) = 6; for n>0, a(n) = 2*a(n-1) - 1.

6, 11, 21, 41, 81, 161, 321, 641, 1281, 2561, 5121, 10241, 20481, 40961, 81921, 163841, 327681, 655361, 1310721, 2621441, 5242881, 10485761, 20971521, 41943041, 83886081, 167772161, 335544321, 671088641, 1342177281, 2684354561, 5368709121, 10737418241

Offset: 0

Author

N. J. A. Sloane, Jun 15 2003

Keywords

• nonn
• easy

Comments

The primes in this sequence are listed in A050526. - M. F. Hasler, Oct 30 2010

An Engel expansion of 2/5 to the base 2 as defined in A181565, with the associated series expansion 2/5 = 2/6 + 2^2/(6*11) + 2^3/(6*11*21) + 2^4/(6*11*21*41) + ... . - Peter Bala, Oct 29 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A020737, A050526, A083683, A083686, A083705, A168596, A181565, A195744.

Programs

Magma

[5*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

Mathematica

NestList[2#-1&,6,40] (* Harvey P. Dale, Jun 23 2017 *)

PARI

a(n)=5<M. F. Hasler, Oct 30 2010

PARI

Vec((6-7*x)/((1-x)*(1-2*x)) + O(x^40)) \\ Colin Barker, Sep 20 2016

Formula

a(n) = 5*2^n + 1. - M. F. Hasler, Oct 30 2010

a(n) = 3*a(n-1) - 2*a(n-2), n>1. - Vincenzo Librandi, Nov 03 2011

G.f.: (6-7*x) / ((1-x)*(1-2*x)). - Colin Barker, Sep 20 2016

E.g.f.: exp(x)*(1 + 5*exp(x)). - Stefano Spezia, Oct 08 2022

Product_{n>=0} (1 + 1/a(n)) = 7/5. - Amiram Eldar, Aug 04 2024