A098878 -id:A098878 - cp's OEIS frontend

A099359 a(n) = (2^n + 1)^3 - 2.

6, 25, 123, 727, 4911, 35935, 274623, 2146687, 16974591, 135005695, 1076890623, 8602523647, 68769820671, 549957165055, 4398851866623, 35187593412607, 281487861809151, 2251851353686015, 18014604668698623, 144116012711149567, 1152924803144876031

Offset: 0

Parthasarathy Nambi, Nov 16 2004

			(2^1 + 1)^3 - 2 = 25.

Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Integer sequence primes.
Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

Cf. A098878.

Table[(2^n + 1)^3 - 2, {n, 19}] (* Robert G. Wilson v, Nov 23 2004 *)

a(n)=(2^n+1)^3-2 \\ Charles R Greathouse IV, Feb 19 2016

Vec((6 - 65*x + 168*x^2 - 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)) + O(x^30)) \\ Colin Barker, Jan 10 2017

From Colin Barker, Jan 10 2017: (Start)
a(n) = (3*2^n + 3*4^n + 8^n - 1).
a(n) = 15*a(n-1) - 70*a(n-2) + 120*a(n-3) - 64*a(n-4) for n>3.
G.f.: (6 - 65*x + 168*x^2 - 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)).
(End)

More terms from Robert G. Wilson v, Nov 23 2004

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

Original entry on oeis.org

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

Offset: 0

Parthasarathy Nambi, Oct 13 2004

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

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

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).

Cf. A091516, A091515, A098878, A091514.

(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 *)

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

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

More terms from Jonathan Vos Post, May 03 2006

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

A117921 Primes of the form (2^k - 1)^3 - 2.

Original entry on oeis.org

3373, 29789, 133432829, 8577357821, 281462092005373

Offset: 1

Jonathan Vos Post, May 03 2006

nonn

Exponent-3 analog of what for exponent 2 is A091516 Carol primes (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1. Hence this is a type of "near-cube primes."

			a(1) = (2^4 - 1)^3 - 2 = 3373 is prime.
a(2) = (2^5 - 1)^3 - 2 = 29789 is prime.
a(3) = (2^9 - 1)^3 - 2 = 133432829 is prime.
a(4) = (2^11 - 1)^3 - 2 = 8577357821 is prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10
Eric Weisstein's World of Mathematics, Near-Square Prime.

Cf. A091516, A091515, A098878, A091514.

Select[(2^Range[20]-1)^3-2,PrimeQ] (* Harvey P. Dale, Oct 22 2016 *)

A098878 INTERSECTION A000040. {(2^k - 1)^3 - 2 iff prime}.

A118558 a(n) = (2^n-1)^4 - 2.

Original entry on oeis.org

-2, -1, 79, 2399, 50623, 923519, 15752959, 260144639, 4228250623, 68184176639, 1095222947839, 17557851463679, 281200199450623, 4501401006735359, 72040003462430719, 1152780773560811519, 18445618199572250623, 295138898083176775679, 4722294425687923097599

Offset: 0

Jonathan Vos Post, May 03 2006

			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.

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

Cf. A091516, A091515, A098878, A091514.

Cf. A093112, A098878.

(2^Range[0, 20] - 1)^4 - 2 (* Paolo Xausa, Apr 19 2024 *)

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

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

G.f.: (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

Offset changed to 0 by Paolo Xausa, Apr 19 2024

cp's OEIS Frontend

A099359 a(n) = (2^n + 1)^3 - 2.

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

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A117921 Primes of the form (2^k - 1)^3 - 2.

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A118558 a(n) = (2^n-1)^4 - 2.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions