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A104745 a(n) = 5^n + n.

%I A104745 #39 Mar 05 2025 12:37:24
%S A104745 1,6,27,128,629,3130,15631,78132,390633,1953134,9765635,48828136,
%T A104745 244140637,1220703138,6103515639,30517578140,152587890641,
%U A104745 762939453142,3814697265643,19073486328144,95367431640645,476837158203146,2384185791015647,11920928955078148,59604644775390649
%N A104745 a(n) = 5^n + n.
%C A104745 Numbers m=5^n+n such that equation x=5^(m-x) has solution x=5^n, see A104744.
%C A104745 No primes of the form 5^n+n for n < 7954. - _Thomas Ordowski_, Oct 28 2013
%C A104745 a(7954) is prime (5560 digits). - _Thomas Ordowski_, May 07 2015
%H A104745 Vincenzo Librandi, <a href="/A104745/b104745.txt">Table of n, a(n) for n = 0..300</a>
%H A104745 Factordb, <a href="http://www.factorization.ath.cx/index.php?query=5%5E7954+%2B+7954">5^7954 + 7954</a>.
%H A104745 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F A104745 From _Vincenzo Librandi_, Jun 16 2013: (Start)
%F A104745 G.f.: (1-x-4*x^2)/((1-5*x)*(1-x)^2).
%F A104745 a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3). (End)
%F A104745 E.g.f.: exp(x)*(exp(4*x) + x). - _Elmo R. Oliveira_, Mar 05 2025
%p A104745 g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..31); # _Zerinvary Lajos_, Jan 09 2009
%t A104745 Table[5^n+n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t A104745 CoefficientList[Series[(1 - x - 4 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 16 2013 *)
%t A104745 LinearRecurrence[{7,-11,5},{1,6,27},30] (* _Harvey P. Dale_, Dec 03 2017 *)
%o A104745 (Magma) I:=[1, 6, 27]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2) +5*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 16 2013
%o A104745 (PARI) a(n)=5^n+n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A104745 Cf. A006127, A058046, A081552, A093324, A104743, A104744, A158879, A181572.
%K A104745 nonn,easy
%O A104745 0,2
%A A104745 _Zak Seidov_, Mar 23 2005
%E A104745 More terms from Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 09 2007