cp's OEIS Frontend

A196305 a(n) = 15*2^n - 1.

%I A196305 #62 Apr 22 2025 04:33:22
%S A196305 14,29,59,119,239,479,959,1919,3839,7679,15359,30719,61439,122879,
%T A196305 245759,491519,983039,1966079,3932159,7864319,15728639,31457279,
%U A196305 62914559,125829119,251658239,503316479,1006632959,2013265919,4026531839,8053063679,16106127359,32212254719,64424509439
%N A196305 a(n) = 15*2^n - 1.
%C A196305 Primes of this sequence are in A196940.
%H A196305 Vincenzo Librandi, <a href="/A196305/b196305.txt">Table of n, a(n) for n = 0..200</a>
%H A196305 Gennady Eremin, <a href="https://arxiv.org/abs/2405.16143">Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant</a>, arXiv:2405.16143 [math.CO], 2024. See pp. 3, 14.
%H A196305 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A196305 a(n) = 15*2^n - 1.
%F A196305 a(n) = A033484(n+1) + A083705(n).
%F A196305 From _Philippe Deléham_, Feb 17 2014: (Start)
%F A196305 a(n) = 2*a(n-1) + 1.
%F A196305 a(n) = 3*a(n-2) - 2*a(n-2).
%F A196305 a(n) = A110286(n) - 1. (End)
%F A196305 From _Elmo R. Oliveira_, Sep 14 2024: (Start)
%F A196305 G.f.: (14 - 13*x)/((1 - x)*(1 - 2*x)).
%F A196305 E.g.f.: exp(x)*(15*exp(x) - 1). (End)
%o A196305 (Magma) [15*2^n -1 : n in [0..50]];
%o A196305 (PARI) a(n)=15<<n-1 \\ _Charles R Greathouse IV_, Oct 08 2011
%Y A196305 Cf. A033484, A083705, A110286 (first differences), A196940.
%K A196305 nonn,easy
%O A196305 0,1
%A A196305 _Brad Clardy_, Oct 07 2011