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%I #30 Jan 01 2024 11:04:43
%S 3,36,54,57,63,96,114,117,123,156,174,177,183,216,234,237,243,276,294,
%T 297,303,336,354,357,363,396,414,417,423,456,474,477,483,516,534,537,
%U 543,576,594,597,603,636,654,657,663,696,714,717,723,756,774,777,783
%N Numbers congruent to {3, 36, 54, 57} mod 60.
%C Numbers n such that the last digit of F(n) is 2 where F(n) is the n-th Fibonacci number.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F Sequence contains numbers of the form: 3+60k, 36+60k, 54+60k, 57+60k, k>=0.
%F 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
%F From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F 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)
%p 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
%t Select[Range[800], MemberQ[{3,36,54,57}, Mod[#,60]]&] (* _Harvey P. Dale_, Apr 07 2013 *)
%o (Magma) [n: n in [0..800] | n mod 60 in [3, 36, 54, 57]]; // _Bruno Berselli_, Jun 14 2016
%Y Cf. A000045, A002265, A003893.
%K nonn,easy
%O 1,1
%A _Benoit Cloitre_, Aug 07 2002
%E Simpler definition from _Ralf Stephan_, Jun 18 2005
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