login
a(n) = (2^n - 1)^5 - 2.
1

%I #15 Nov 03 2016 13:55:58

%S -2,-1,241,16805,759373,28629149,992436541,33038369405,1078203909373,

%T 34842114263549,1120413075641341,35940921946155005,

%U 1151514816750309373,36870975646169341949,1180231376725002502141,37773167607267111108605,1208833588708967444709373

%N a(n) = (2^n - 1)^5 - 2.

%C 5th-power analog of what for exponent 2 is A093112 (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1 and exponent 3 is A098878 (2^n - 1)^3 - 2. Primes include a(n) for n = 0, 2, 5, 6. These are "near-5th-power prime." Semiprimes include a(n) for n = 3, 8, 9, 10, 13, 15, 21, 29, 33, 40. - _Jonathan Vos Post_, May 03 2006

%H Harvey P. Dale, <a href="/A098879/b098879.txt">Table of n, a(n) for n = 0..664</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime.</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (63, -1302, 11160, -41664, 64512, -32768).

%F G.f.: (-2+125*x-2300*x^2+22640*x^3-57728*x^4+66560*x^5)/((-1+x)(-1+32*x)(-1+16*x)(-1+8*x)(-1+4*x)(-1+2*x)). - _R. J. Mathar_, Nov 14 2007

%e If n=2, (2^2 - 1)^5 - 2 = 241 (a prime).

%t (2^Range[0,20]-1)^5-2 (* or *) LinearRecurrence[{63,-1302,11160,-41664,64512,-32768},{-2,-1,241,16805,759373,28629149},20] (* _Harvey P. Dale_, Nov 03 2016 *)

%o (PARI) a(n)=(2^n-1)^5-2 \\ _Charles R Greathouse IV_, Feb 19 2016

%Y Cf. A091516, A091515, A098878, A091514.

%K easy,sign

%O 0,1

%A _Parthasarathy Nambi_, Oct 13 2004

%E More terms from _Jonathan Vos Post_, May 03 2006

%E Edited by _N. J. A. Sloane_, Sep 30 2007