A098879 a(n) = (2^n - 1)^5 - 2.

-2, -1, 241, 16805, 759373, 28629149, 992436541, 33038369405, 1078203909373, 34842114263549, 1120413075641341, 35940921946155005, 1151514816750309373, 36870975646169341949, 1180231376725002502141, 37773167607267111108605, 1208833588708967444709373

Offset: 0

Author

Parthasarathy Nambi, Oct 13 2004

Keywords

• easy
• sign

Comments

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..664
• Eric Weisstein's World of Mathematics, Near-Square Prime.
• Index entries for linear recurrences with constant coefficients, signature (63, -1302, 11160, -41664, 64512, -32768).

Crossrefs

Cf. A091516, A091515, A098878, A091514.

Programs

Mathematica

(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 *)

PARI

a(n)=(2^n-1)^5-2 \\ Charles R Greathouse IV, Feb 19 2016

Formula

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

Extensions

More terms from Jonathan Vos Post, May 03 2006

Edited by N. J. A. Sloane, Sep 30 2007