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A072682 Numbers congruent to {3, 36, 54, 57} mod 60. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

a(n) = (1/4)*{22*(n mod 4)+7*[(n+1) mod 4]-8*[(n+2) mod 4]+79*[(n+3) mod 4]} + 60*A002265. - Paolo P. Lava, Nov 05 2007

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

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Last modified August 17 17:32 EDT 2017. Contains 290651 sequences.