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, 70368727400449, 281474943156225, 1125899839733761

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..26.

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)

From Elmo R. Oliveira, Sep 17 2025: (Start)

E.g.f.: (-1 + 16*x + 16*x^2 + 4*exp(x) - 4*exp(2*x) + exp(4*x))/4.

a(n) = A000225(n-1)^2 for n > 2. (End)

Example

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

Crossrefs

Cf. A000225, 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

More terms from Elmo R. Oliveira, Sep 17 2025

Status

approved