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A062709 a(n) = 2^n + 3.

%I A062709 #38 May 07 2023 05:40:17
%S A062709 4,5,7,11,19,35,67,131,259,515,1027,2051,4099,8195,16387,32771,65539,
%T A062709 131075,262147,524291,1048579,2097155,4194307,8388611,16777219,
%U A062709 33554435,67108867,134217731,268435459,536870915,1073741827,2147483651,4294967299,8589934595,17179869187
%N A062709 a(n) = 2^n + 3.
%C A062709 Written in binary a(n) is 1000...00011 for n > 1.
%C A062709 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 A062709 Vincenzo Librandi, <a href="/A062709/b062709.txt">Table of n, a(n) for n = 0..1000</a>
%H A062709 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A062709 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 A062709 G.f.: (4 - 7*x)/((1 - 2*x)*(1 - x)).
%F A062709 a(n) = A173921(A000051(n+1)). - _Reinhard Zumkeller_, Mar 04 2010
%F A062709 E.g.f.: exp(x)*(3 + exp(x)). - _Stefano Spezia_, May 06 2023
%e A062709 a(3) = 2^3 + 3 = 8 + 3 = 11.
%e A062709 a(4) = 2^4 + 3 = 16 + 3 = 19.
%t A062709 LinearRecurrence[{3, -2}, {4, 5}, 40] (* _Vincenzo Librandi_, Jan 31 2012 *)
%t A062709 NestList[2 * # - 3 &, 4, 20] (* _Zak Seidov_, Mar 28 2015 *)
%t A062709 2^Range[0, 29] + 3 (* _Alonso del Arte_, Mar 28 2015 *)
%o A062709 (Sage) [gaussian_binomial(n,1,2)+4 for n in range(0,32)] # _Zerinvary Lajos_, May 31 2009
%o A062709 (PARI) a(n)=2^n+3 \\ _Charles R Greathouse IV_, Jan 30 2012
%o A062709 (Magma) [2^n+3: n in [0..40]] // _Vincenzo Librandi_, Jan 31 2012
%Y A062709 Primes in this sequence are A057733.
%Y A062709 Cf. A000051, A000079, A000120, A000225, A004119, A030101, A052548, A173921.
%K A062709 nonn,easy
%O A062709 0,1
%A A062709 _Henry Bottomley_, Jul 13 2001