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A168596
a(n) = 2*a(n-1) - 1 with a(0)=14.
10
14, 27, 53, 105, 209, 417, 833, 1665, 3329, 6657, 13313, 26625, 53249, 106497, 212993, 425985, 851969, 1703937, 3407873, 6815745, 13631489, 27262977, 54525953, 109051905, 218103809, 436207617, 872415233, 1744830465, 3489660929
OFFSET
0,1
COMMENTS
An Engel expansion of 2/13 to the base 2 as defined in A181565, with the associated series expansion 2/13 = 2/14 + 2^2/(14*27) + 2^3/(14*27*53) + 2^4/(14*27*53*105) + .... - Peter Bala, Oct 29 2013
FORMULA
From Vincenzo Librandi, Nov 03 2011: (Start)
a(n) = 13*2^n + 1.
a(n) = 3*a(n-1) - 2*a(n-2). (End)
From G. C. Greubel, Jul 27 2016: (Start)
G.f.: (14 - 15*x)/((1-x)*(1-2*x)).
E.g.f.: exp(x) + 13*exp(2*x). (End)
MATHEMATICA
s=14; lst={s}; Do[s=s+(s-1); AppendTo[lst, s], {n, 5!}]; lst
NestList[2#-1&, 14, 30] (* Harvey P. Dale, Jul 22 2014 *)
PROG
(Magma) [13*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset changed from 1 to 0 by Vincenzo Librandi, Nov 03 2011
STATUS
approved