|
Search: id:A098879
|
|
| |
|
| -2, -1, 241, 16805, 759373, 28629149, 992436541, 33038369405, 1078203909373, 34842114263549, 1120413075641341, 35940921946155005, 1151514816750309373, 36870975646169341949, 1180231376725002502141, 37773167607267111108605, 1208833588708967444709373
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
5th power analogue of Carol numbers A091515. Exponent 5 analogue of what for exponent 2 is A091516 Carol primes (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 (jvospost2(AT)yahoo.com), May 03 2006
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Near-Square Prime.
|
|
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 (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
|
|
EXAMPLE
|
If n=2, (2^2 - 1)^5 - 2 = 241 (a prime)
|
|
CROSSREFS
|
Cf. A091516, A091515, A098878, A091514.
Sequence in context: A101923 A010788 A016448 this_sequence A087037 A036109 A098940
Adjacent sequences: A098876 A098877 A098878 this_sequence A098880 A098881 A098882
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Oct 13 2004
|
|
EXTENSIONS
|
More terms from Jonathan Vos Post (jvospost2(AT)yahoo.com), May 03 2006
Edited by njas, Sep 30 2007
|
|
|
Search completed in 0.002 seconds
|
