A112652 a(n) squared is congruent to a(n) (mod 12).

0, 1, 4, 9, 12, 13, 16, 21, 24, 25, 28, 33, 36, 37, 40, 45, 48, 49, 52, 57, 60, 61, 64, 69, 72, 73, 76, 81, 84, 85, 88, 93, 96, 97, 100, 105, 108, 109, 112, 117, 120, 121, 124, 129, 132, 133, 136, 141, 144, 145, 148, 153, 156, 157, 160, 165, 168, 169, 172, 177, 180

Offset

0,3

Comments

Numbers m such that A000217(3*m)/2 + A000217(2*m)/3 is an integer. - Bruno Berselli, Jul 01 2016

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Formula

From R. J. Mathar, Sep 25 2009: (Start)

G.f.: x*(1 + 2*x + 3*x^2)/((x^2 + 1)*(x - 1)^2).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4).

a(n) = A087960(n) + 3*n - 1. (End)

Example

a(3) = 9 because 9^2 = 81 = 6*12 + 9, hence 81 == 9 (mod 12).

Maple

m = 12 for n = 1 to 300 if n^2 mod m = n mod m then print n; next n

Mathematica

Select[Range[0, 180], Mod[#^2, 12] == Mod[#, 12] &] (* or *)
CoefficientList[Series[x (1 + 2 x + 3 x^2)/((x^2 + 1) (x - 1)^2), {x, 0, 60}], x] (* Michael De Vlieger, Jul 01 2016 *)

Prog

(PARI) is(n)=(n^2-n)%12==0 \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A000217, A087960.

Sequence in context: A368742 A312848 A010413 * A272933 A367929 A243650

Adjacent sequences: A112649 A112650 A112651 * A112653 A112654 A112655

Keyword

nonn,easy

Author

Jeremy Gardiner, Dec 28 2005

Status

approved