A076936 a(1) = 1; then the smallest number different from its predecessor such that the n-th partial product is an n-th power.

1, 4, 2, 32, 4, 256, 8, 2048, 16, 16384, 32, 131072, 64, 1048576, 128, 8388608, 256, 67108864, 512, 536870912, 1024, 4294967296, 2048, 34359738368, 4096, 274877906944, 8192, 2199023255552, 16384, 17592186044416, 32768

Offset: 1

Author

Amarnath Murthy, Oct 19 2002

Keywords

• nonn

Comments

Or "such that the geometric mean of the first n terms is an integer." (Without the "different from its predecessor" requirement, the trivial sequence 1,4,2,2,2,2,2,... would have resulted.)

Links

• Robert Israel, Table of n, a(n) for n = 1..2209
• Index entries for linear recurrences with constant coefficients, signature (0, 10, 0, -16).

Crossrefs

Cf. A014682, A016116.

Programs

Maple

seq(op([2^k,2^(3*k+2)]),k=0..20); # Robert Israel, Nov 27 2016

Mathematica

CoefficientList[Series[x (1 + 4 x - 8 x^2 - 8 x^3)/(1 - 10 x^2 + 16 x^4), {x, 0, 31}], x] (* Michael De Vlieger, Nov 24 2017 *)
LinearRecurrence[{0,10,0,-16},{1,4,2,32},40] (* Harvey P. Dale, Mar 20 2024 *)

Formula

From Robert Israel, Nov 27 2016: (Start)

a(n) = 2^A014682(n-1).

G.f.: x*(1+4*x-8*x^2-8*x^3)/(1-10*x^2+16*x^4). (End)

Extensions

More terms from Sam Alexander, Nov 15 2003