A072682 Numbers congruent to {3, 36, 54, 57} mod 60.

3, 36, 54, 57, 63, 96, 114, 117, 123, 156, 174, 177, 183, 216, 234, 237, 243, 276, 294, 297, 303, 336, 354, 357, 363, 396, 414, 417, 423, 456, 474, 477, 483, 516, 534, 537, 543, 576, 594, 597, 603, 636, 654, 657, 663, 696, 714, 717, 723, 756, 774, 777, 783

Offset

1,1

Comments

Numbers n such that the last digit of F(n) is 2 where F(n) is the n-th Fibonacci number.

Links

Table of n, a(n) for n=1..53.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

Sequence contains numbers of the form: 3+60k, 36+60k, 54+60k, 57+60k, k>=0.

G.f.: 3*x*(1 + 11*x + 6*x^2 + x^3 + x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = 15*n + 3*(1+i)*((1-i)*i^(2*n) - (5+2*i)*i^(-n) + (2+5*i)*i^n)/4 where i=sqrt(-1). (End)

Maple

A072682:=n->15*n+3*(1+I)*((1-I)*I^(2*n)-(5+2*I)*I^(-n)+(2+5*I)*I^n)/4: seq(A072682(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[800], MemberQ[{3, 36, 54, 57}, Mod[#, 60]]&] (* Harvey P. Dale, Apr 07 2013 *)

Prog

(Magma) [n: n in [0..800] | n mod 60 in [3, 36, 54, 57]];  // Bruno Berselli, Jun 14 2016

Crossrefs

Cf. A000045, A002265, A003893.

Sequence in context: A105758 A214852 A113799 * A158207 A227032 A153448

Adjacent sequences: A072679 A072680 A072681 * A072683 A072684 A072685

Keyword

nonn,easy

Author

Benoit Cloitre, Aug 07 2002

Extensions

Simpler definition from Ralf Stephan, Jun 18 2005

Status

approved