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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 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 September 18 23:05 EDT 2021. Contains 347548 sequences. (Running on oeis4.)