A099481 -id:A099481 - cp's OEIS frontend

A024012 a(n) = 2^n - n^2.

1, 1, 0, -1, 0, 7, 28, 79, 192, 431, 924, 1927, 3952, 8023, 16188, 32543, 65280, 130783, 261820, 523927, 1048176, 2096711, 4193820, 8388079, 16776640, 33553807, 67108188, 134216999, 268434672, 536870071, 1073740924, 2147482687, 4294966272, 8589933503, 17179868028, 34359737143

Offset: 0

N. J. A. Sloane

The sequence 2^(n-2) - (n-2)^2, n=7,8,... enumerates the number of non-isomorphic sequences of length n, with entries from {1,2,3} and no two adjacent entries the same, that contain each of the thirteen rankings of three players (111, 121, 112, 211, 122, 212, 221, 123, 132, 213, 231, 312, 321) as embedded order isomorphic subsequences. See the arXiv paper below for proof. If n=7, these sequences are 1213121, 1213212, 1231213, 1231231,1231321, 1232123, and 1232132, and for each case, there are 3!=6 isomorphs. - Anant Godbole, Feb 20 2013

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 92.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Anant Godbole and Martha Liendo, Waiting time distribution for the emergence of superpatterns, arxiv 1302.4668 [math.PR], 2013.
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Cf. A072180 (2^n - n^2 is prime), A075896 (primes of the form 2^n - n^2), A099481 (2^n - n^2 is a semiprime), A099482 (semiprimes of the form 2^n - n^2).

[2^n-n^2: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011

seq(2^n-n^2, n=0..35); # Zerinvary Lajos, Jul 01 2007

CoefficientList[Series[(1 - 4*x + 4*x^2 + x^3)/((1 - x)^3(1 - 2x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 13 2012 *)
Table[2^n - n^2, {n, 0, 39}] (* Alonso del Arte, Dec 16 2012 *)

A024012(n):=2^n-n^2$ makelist(A024012(n),n,0,20); /* Martin Ettl, Dec 18 2012 */

a(n)=2^n-n^2 \\ Charles R Greathouse IV, Apr 17 2012

G.f.: (1 - 4*x + 4*x^2 + x^3)/((1 - 2*x)*(1 - x)^3). - Vincenzo Librandi, Jul 13 2012

a(n) = 5*a(n - 1) - 9*a(n - 2) + 7*a(n - 3) - 2*a(n - 4). - Vincenzo Librandi, Jul 13 2012

More terms from Hugo Pfoertner, Oct 18 2004

A099482 Semiprimes of the form 2^k - k^2.

Original entry on oeis.org

1927, 8023, 32543, 2096711, 8388079, 137438952103, 549755812367, 2199023253871, 8796093020359, 140737488353119, 562949953418911, 36028797018960943, 147573952589676408439, 37778931862957161703943

Offset: 1

Hugo Pfoertner, Oct 18 2004

nonn

			a(2) = 8023 because 8023 = 71*113 = 2^13 - 13^2 = 2^A099481(2) - A099481(2)^2.

Hugo Pfoertner, Table of n, a(n) for n = 1..36
Dario Alpern, Factorization using the Elliptic Curve Method.

Cf. A024012 2^n-n^2, A099481 2^k-k^2 is a semiprime, A072180 2^k-k^2 is prime, A075896 primes of the form 2^k-k^2.

Select[Table[2^n - n^2, {n, 100}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 21 2012 *)

cp's OEIS Frontend

A024012 a(n) = 2^n - n^2.

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