A088041 Smallest k such that k^4 - 1 is divisible by an n-th power, k > 1.

2, 3, 3, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3323

Robert Israel, Proof of conjectured formula

Formula

a(n) = A088040(n)^(1/4).

Apparently a(n) = 2^(n-2) - 1 for n>3.

Conjecture: a(n) = 3*a(n-1)-2*a(n-2) for n>5. G.f.: x*(4*x^4-2*x^2-3*x+2) / ((x-1)*(2*x-1)). [Colin Barker, Feb 05 2013]

Conjectures confirmed (see link). - Robert Israel, Aug 19 2019

Maple

2, 3, 3, seq(2^(n-2)-1, n=4...40); # Robert Israel, Aug 19 2019

Mathematica

{2, 3, 3}~Join~Array[2^(# - 2) - 1 &, 30, 4] (* Michael De Vlieger, Aug 19 2019 *)

Crossrefs

Cf. A088040.

Sequence in context: A109833 A132005 A222292 * A334579 A199457 A361378

Adjacent sequences: A088038 A088039 A088040 * A088042 A088043 A088044

Keyword

nonn

Author

Amarnath Murthy, Sep 19 2003

Extensions

Corrected and extended by Ray Chandler, Oct 04 2003

Status

approved