login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118558 a(n) = (2^n-1)^4 - 2. 0
-2, -1, 79, 2399, 50623, 923519, 15752959, 260144639, 4228250623, 68184176639, 1095222947839, 17557851463679, 281200199450623, 4501401006735359, 72040003462430719, 1152780773560811519, 18445618199572250623, 295138898083176775679, 4722294425687923097599 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Exponent-4 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, 3, 11, 57; a type of "near-biquadratic primes." No more primes through (2^100-1)^4 - 2. Semiprimes include a(n) for n = 5, 6, 8, 10, 13, 14, 19, 20, 21, 25, 33, 35, 36, 40, 43, 51, 53, 63.

LINKS

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Near-Square Prime.

Index entries for linear recurrences with constant coefficients, signature (31,-310,1240,-1984,1024).

FORMULA

a(n) = (2^n - 1)^4 - 2.

G.f.: x*(1984*x^4-2120*x^3+510*x^2-61*x+2) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(16*x-1)). - Colin Barker, Apr 30 2013

EXAMPLE

a(0) = (2^0 - 1)^4 - 2 = 0^4 - 2 = -2.

a(1) = (2^1 - 1)^4 - 2 = 1^4 - 2 = -1.

a(2) = (2^2 - 1)^4 - 2 = 3^4 - 2 = 79 (prime).

a(3) = (2^3 - 1)^4 - 2 = 7^4 - 2 = 2399 (prime).

a(11) = (2^11 - 1)^4 - 2 = 17557851463679 (prime).

a(57) = (2^57 - 1)^4 - 2 = 431359146674410224742050828377557509468732765984721170947417969786879 (prime).

PROG

(PARI) a(n)=(2^n-1)^4-2 \\ Charles R Greathouse IV, Feb 19 2016

CROSSREFS

Cf. A091516, A091515, A098878, A091514.

Sequence in context: A247793 A067276 A118580 * A095837 A095835 A147805

Adjacent sequences:  A118555 A118556 A118557 * A118559 A118560 A118561

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 03 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)