A147540 Numbers whose binary representation is the concatenation of 2n-1 digits 1, n digits 0 and 2n-1 digits 1.

5, 231, 7967, 260223, 8372735, 268306431, 8588894207, 274869551103, 8796026044415, 281474440364031, 9007194961870847, 288230341800361983, 9223371762010423295, 295147902980463788031, 9444732948147641253887

Offset: 1

Author

Omar E. Pol, Nov 06 2008

Keywords

• base
• easy
• nonn

Comments

a(n) is the number whose binary representation is A138826(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..660

Crossrefs

Cf. A138826.

Programs

GAP

List([1..20], n-> 2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1); # G. C. Greubel, Jan 12 2020

Magma

[2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1: n in [1..20]]; // G. C. Greubel, Jan 12 2020

Maple

seq( 2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1, n=1..20); # G. C. Greubel, Jan 12 2020

Mathematica

Table[FromDigits[Join[Table[1, {2n-1}], Table[0, {n}], Table[1, {2n-1}]], 2], {n,15}] (* Stefan Steinerberger, Nov 11 2008 *)

PARI

vector(20, n, 2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1) \\ G. C. Greubel, Jan 12 2020

Sage

[2^(5*n-2) -2^(3*n-1) +2^(2*n-1) -1 for n in (1..20)] # G. C. Greubel, Jan 12 2020

Formula

From R. J. Mathar, Nov 09 2008: (Start)

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

G.f.: x*(5 +6*x -128*x^2 +768*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-32*x)). (End)

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Nov 11 2008