A095768 a(n) = 2^(n+1) - n.

3, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, 32754, 65521, 131056, 262127, 524270, 1048557, 2097132, 4194283, 8388586, 16777193, 33554408, 67108839, 134217702, 268435429, 536870884, 1073741795, 2147483618

Offset: 1

Author

Benoit Cloitre, Jun 05 2004

Keywords

• nonn
• easy

Comments

Least k such that valuation(A004001(k),2) = n.

Apart from initial term, row sums of triangle A135087.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A000247, A004001, A095767, A132045, A135087.

Programs

Mathematica

Table[2^(n + 1) - n, {n, 0, 31}] (* Robert G. Wilson v Jun 12 2004 *)
LinearRecurrence[{4,-5,2},{3,6,13},40] (* Harvey P. Dale, Jan 02 2012 *)

Maxima

A095768(n):=2^(n+1)-n$
makelist(A095768(n),n,1,30); /* Martin Ettl, Nov 08 2012 */

PARI

a(n)=2^(n+1)-n \\ Charles R Greathouse IV, Oct 16 2015

Formula

From R. J. Mathar, Apr 30 2008: (Start)

O.g.f.: -x*(3-6*x+48*x^2)/((-1+x)^2*(-1+2*x)).

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). (End)

a(n) = A000247(n+1) + 3 = 2^(n+1) - n. - Martin Ettl, Nov 08 2012

E.g.f.: exp(x)*(2*exp(x) - x) - 2. - Elmo R. Oliveira, Mar 08 2025