A116452 -id:A116452 - cp's OEIS frontend

A116454 Smallest m such that A116452(m) = n.

0, 2, 9, 25, 59, 129, 271, 557, 1131, 2281, 4583, 9189, 18403, 36833, 73695, 147421, 294875, 589785, 1179607, 2359253, 4718547, 9437137, 18874319, 37748685, 75497419, 150994889, 301989831, 603979717, 1207959491, 2415919041

Offset: 1

Reinhard Zumkeller, Feb 16 2006

A116451(a(n)) = A116453(n);

Primes include a(2) = 2, a(5) = 59, a(7) = 271, a(8) = 557, a(10) = 2281, a(11) = 4583, a(14) = 36833. - Jonathan Vos Post, Feb 20 2006

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

Join[{0},RecurrenceTable[{a[1]==2,a[n]==2(a[n-1]+n)+1},a[n],{n,30}]] (* or *) Join[{0},LinearRecurrence[{4,-5,2},{2,9,25},30]] (* Harvey P. Dale, Jul 18 2011 *)

a(n+1) = (a(n) + n) * 2 + 1 for n>1.
From Harvey P. Dale, Jul 18 2011: (Start)
a(0)=0, a(1)=2, a(2)=9, a(3)=25, a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3).
G.f.: (x-2)*x^2*(x+1)/((x-1)^2*(2*x-1)). (End)

A116451 Numbers having fewer prime factors than at least one smaller number.

Original entry on oeis.org

5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset: 0

Reinhard Zumkeller, Feb 16 2006

nonn

Complement of A029744.

Numbers whose odd part is greater than 3. - Peter Munn, Aug 12 2020

Cf. A029744, A116452, A001222.

A116452(n) = A001222(a(n)).

The offset should really be 1, since this is a list, but that change would also require a complete rewrite of A116454, plus changes to A116453. So for the moment let's leave this with offset 0. - N. J. A. Sloane, Aug 17 2020

cp's OEIS Frontend

A116454 Smallest m such that A116452(m) = n.

Views

Author

Keywords

Comments

Links

Programs

Mathematica

Formula