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A226201 a(n) = 8^n + n.

%I A226201 #32 Mar 06 2025 01:54:56
%S A226201 1,9,66,515,4100,32773,262150,2097159,16777224,134217737,1073741834,
%T A226201 8589934603,68719476748,549755813901,4398046511118,35184372088847,
%U A226201 281474976710672,2251799813685265,18014398509482002,144115188075855891,1152921504606846996,9223372036854775829
%N A226201 a(n) = 8^n + n.
%C A226201 Smallest prime of this form is a(101). - _Bruno Berselli_, Jun 17 2013
%H A226201 Vincenzo Librandi, <a href="/A226201/b226201.txt">Table of n, a(n) for n = 0..300</a>
%H A226201 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).
%F A226201 G.f.: (-1+x+7*x^2)/((8*x-1)*(x-1)^2).
%F A226201 a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).
%F A226201 E.g.f.: exp(x)*(exp(7*x) + x). - _Elmo R. Oliveira_, Mar 05 2025
%t A226201 Table[8^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(-1 + x + 7 x^2) / ((8 x - 1) (x - 1)^2), {x, 0, 30}], x]
%t A226201 LinearRecurrence[{10,-17,8},{1,9,66},30] (* _Harvey P. Dale_, Aug 11 2015 *)
%o A226201 (Magma) [8^n+n: n in [0..30]];
%o A226201 (Magma) I:=[1, 9, 66]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]];
%o A226201 (PARI) a(n)=8^n+n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A226201 Cf. numbers of the form k^n+n: A006127 (k=2), A104743 (k=3), A158879 (k=4), A104745 (k=5), A226200 (k=6), A226199 (k=7), this sequence (k=8), A226202 (k=9), A081552 (k=10), A226737 (k=11).
%Y A226201 Cf. A199555 (first differences).
%K A226201 nonn,easy
%O A226201 0,2
%A A226201 _Vincenzo Librandi_, Jun 16 2013