A099482 -id:A099482 - 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

A099481 Numbers k such that 2^k - k^2 is a semiprime.

Original entry on oeis.org

11, 13, 15, 21, 23, 37, 39, 41, 43, 47, 49, 55, 67, 75, 103, 105, 133, 147, 153, 161, 163, 177, 201, 209, 221, 239, 249, 263, 311, 335, 355, 397, 413, 421, 437, 447, 583, 617, 775, 807

Offset: 1

Hugo Pfoertner, Oct 18 2004

The smaller prime factor of the 125-digit semiprime 2^413 - 413^2 has 40 digits; for the 127-digit semiprime 2^421 - 421^2 the smaller prime factor has 45 digits. The next term is >= 583. - Hugo Pfoertner, Oct 14 2007
The factorization of the 176-decimal-digit composite 2^583 - 583^2 using SNFS in YAFU took 55000 seconds on 4 cores of an i5-2400 CPU @ 3.10GHz. a(38) >= 617. - Hugo Pfoertner, Jul 23 2019
a(41) >= 827. - Hugo Pfoertner, Jul 26 2019

			a(1) = 11 because 2^11 - 11^2 = 1927 = 41*47.

Dario Alpern, Factorization using the Elliptic Curve Method.
factordb, Status of 2^583-583^2 in factordb.com.
factordb, Status of 2^617-617^2 in factordb.com.
factordb, Status of 2^827-827^2 in factordb.com.
YAFU, Automated integer factorization.

Cf. A024012 (2^n-n^2), A099482 (semiprimes of the form 2^n-n^2), A072180 (2^n-n^2 is prime), A075896 (primes of the form 2^n-n^2).

More terms from Hugo Pfoertner, Oct 14 2007

a(37)-a(40) from Hugo Pfoertner, Jul 26 2019

cp's OEIS Frontend

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

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