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A098879 a(n) = (2^n - 1)^5 - 2. 1
-2, -1, 241, 16805, 759373, 28629149, 992436541, 33038369405, 1078203909373, 34842114263549, 1120413075641341, 35940921946155005, 1151514816750309373, 36870975646169341949, 1180231376725002502141, 37773167607267111108605, 1208833588708967444709373 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A258819 A337051 A016448 * A331818 A261437 A012867
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

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)