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

0,1

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

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).

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A091516, A091515, A098878, A091514.

Sequence in context: A258819 A337051 A016448 * A331818 A261437 A012867

Adjacent sequences: A098876 A098877 A098878 * A098880 A098881 A098882

Keyword

easy,sign

Author

Parthasarathy Nambi, Oct 13 2004

Extensions

More terms from Jonathan Vos Post, May 03 2006

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

Status

approved