|
%I #38 May 07 2023 05:40:17
%S 4,5,7,11,19,35,67,131,259,515,1027,2051,4099,8195,16387,32771,65539,
%T 131075,262147,524291,1048579,2097155,4194307,8388611,16777219,
%U 33554435,67108867,134217731,268435459,536870915,1073741827,2147483651,4294967299,8589934595,17179869187
%N a(n) = 2^n + 3.
%C Written in binary a(n) is 1000...00011 for n > 1.
%C For n >= 2, a(n) is the minimal k for which A000120(k(2^n-1)) is not multiple of n. - _Vladimir Shevelev_, Jun 05 2009
%H Vincenzo Librandi, <a href="/A062709/b062709.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 2a(n-1) - 3 = A052548(n) + 1 = A000051(n) + 2 = A000079(n) + 3 = A000225(n) + 4 = A030101(A004119(n)) for n > 1.
%F G.f.: (4 - 7*x)/((1 - 2*x)*(1 - x)).
%F a(n) = A173921(A000051(n+1)). - _Reinhard Zumkeller_, Mar 04 2010
%F E.g.f.: exp(x)*(3 + exp(x)). - _Stefano Spezia_, May 06 2023
%e a(3) = 2^3 + 3 = 8 + 3 = 11.
%e a(4) = 2^4 + 3 = 16 + 3 = 19.
%t LinearRecurrence[{3, -2}, {4, 5}, 40] (* _Vincenzo Librandi_, Jan 31 2012 *)
%t NestList[2 * # - 3 &, 4, 20] (* _Zak Seidov_, Mar 28 2015 *)
%t 2^Range[0, 29] + 3 (* _Alonso del Arte_, Mar 28 2015 *)
%o (Sage) [gaussian_binomial(n,1,2)+4 for n in range(0,32)] # _Zerinvary Lajos_, May 31 2009
%o (PARI) a(n)=2^n+3 \\ _Charles R Greathouse IV_, Jan 30 2012
%o (Magma) [2^n+3: n in [0..40]] // _Vincenzo Librandi_, Jan 31 2012
%Y Primes in this sequence are A057733.
%Y Cf. A000051, A000079, A000120, A000225, A004119, A030101, A052548, A173921.
%K nonn,easy
%O 0,1
%A _Henry Bottomley_, Jul 13 2001
|
