A226201 - OEIS

%I #25 Feb 12 2024 13:12:22

%S 1,9,66,515,4100,32773,262150,2097159,16777224,134217737,1073741834,

%T 8589934603,68719476748,549755813901,4398046511118,35184372088847,

%U 281474976710672,2251799813685265,18014398509482002,144115188075855891,1152921504606846996

%N a(n) = 8^n + n.

%C Smallest prime of this form is a(101). - _Bruno Berselli_, Jun 17 2013

%H Vincenzo Librandi, <a href="/A226201/b226201.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).

%F G.f.: (-1+x+7*x^2)/((8*x-1)*(x-1)^2).

%F a(n) = 10*a(n-1)-17*a(n-2)+8*a(n-3).

%t 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 LinearRecurrence[{10,-17,8},{1,9,66},30] (* _Harvey P. Dale_, Aug 11 2015 *)

%o (Magma) [8^n+n: n in [0..30]]; /* or */ 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 (PARI) a(n)=8^n+n \\ _Charles R Greathouse IV_, Oct 07 2015

%Y 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 Cf. A199555 (first differences).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jun 16 2013