A088037 Smallest square k == 1 (mod some n-th power), k > 1.

4, 9, 9, 49, 225, 961, 3969, 16129, 65025, 261121, 1046529, 4190209, 16769025, 67092481, 268402689, 1073676289, 4294836225, 17179607041, 68718952449, 274876858369, 1099509530625, 4398042316801, 17592177655809

Offset

1,1

Comments

From a(2) onwards the n-th power that divides a(n) -1 is 2^n ===> Second term onwards same as A060867 i.e. a(n+1) = (2^n-1)^2.

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

From Colin Barker, Feb 05 2013: (Start)

a(n) = (2^n-2)^2/4 for n>2.

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>5.

G.f.: x*(2*x+1)*(32*x^3-56*x^2+27*x-4) / ((x-1)*(2*x-1)*(4*x-1)). (End)

Example

a(6) = 961 and 960 = 64*15.

Crossrefs

Cf. A060867.

Sequence in context: A091657 A156047 A171001 * A071768 A301478 A173297

Adjacent sequences: A088034 A088035 A088036 * A088038 A088039 A088040

Keyword

nonn,easy

Author

Amarnath Murthy, Sep 19 2003

Extensions

More terms from Ray Chandler, Oct 04 2003

Status

approved