A261871 Numbers of the form (2*j-1)*(2^k-1); j>=1, k>=2.

3, 7, 9, 15, 21, 27, 31, 33, 35, 39, 45, 49, 51, 57, 63, 69, 75, 77, 81, 87, 91, 93, 99, 105, 111, 117, 119, 123, 127, 129, 133, 135, 141, 147, 153, 155, 159, 161, 165, 171, 175, 177, 183, 189, 195, 201, 203, 207, 213, 217, 219, 225, 231, 237, 243, 245, 249, 255, 259, 261, 267, 273, 279, 285, 287, 291, 297, 301

Offset: 1

Author

Bob Selcoe, Sep 04 2015

Keywords

• nonn
• easy

Comments

Odd numbers complementary to A185208.

Lim_{n->inf.} a(n)/n > 6/(1 + Sum_{j>=1} (2/(2^(2j+1)-1))) ~ 4.375745.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A185208.

Note that A191131, A261524, A261871, and A282572 are very similar and easily confused with each other.

Programs

Mathematica

lmt = 310; Take[ Union@ Flatten@ Table[ (2j - 1)(2^k - 1), {j, lmt/4}, {k, 2, 1 + Log2[ lmt/(2j)] }], 68] (* Michael De Vlieger, Sep 04 2015 *) (* and modified by Robert G. Wilson v, Sep 05 2015 *)

PARI

list(lim)=my(v=List(),t); for(k=2,logint(lim\1+1,2), t=2^k-1; forstep(j=1,lim\t,2, listput(v,t*j))); Set(v) \\ Charles R Greathouse IV, Sep 05 2015

Formula

2n < a(n) < 5n. For n > 51, 4.3n < a(n) < 4.5n. - Charles R Greathouse IV, Sep 05 2015