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%I #36 Sep 08 2022 08:45:17
%S 1,6,27,128,629,3130,15631,78132,390633,1953134,9765635,48828136,
%T 244140637,1220703138,6103515639,30517578140,152587890641,
%U 762939453142,3814697265643,19073486328144,95367431640645,476837158203146
%N a(n) = 5^n + n.
%C Numbers m=5^n+n such that equation x=5^(m-x) has solution x=5^n, see A104744.
%C No primes of the form 5^n+n for n < 7954. - _Thomas Ordowski_, Oct 28 2013
%C a(7954) is prime (5560 digits). - _Thomas Ordowski_, May 07 2015
%H Vincenzo Librandi, <a href="/A104745/b104745.txt">Table of n, a(n) for n = 0..300</a>
%H Factordb, <a href="http://www.factorization.ath.cx/index.php?query=5%5E7954+%2B+7954">5^7954 + 7954</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F G.f.: (1-x-4*x^2)/((1-5*x)(1-x)^2). - _Vincenzo Librandi_, Jun 16 2013
%F a(n) = 7*a(n-1)-11*a(n-2)+5*a(n-3). - _Vincenzo Librandi_, Jun 16 2013
%p 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 Table[5^n+n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t CoefficientList[Series[(1 - x - 4 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 16 2013 *)
%t LinearRecurrence[{7,-11,5},{1,6,27},30] (* _Harvey P. Dale_, Dec 03 2017 *)
%o (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 (PARI) a(n)=5^n+n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A104744, A006127, A104743, A158879, A081552, A058046, A181572, A093324.
%K nonn,easy
%O 0,2
%A _Zak Seidov_, Mar 23 2005
%E More terms from Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 09 2007
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