cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A072682 #30 Jan 01 2024 11:04:43
%S A072682 3,36,54,57,63,96,114,117,123,156,174,177,183,216,234,237,243,276,294,
%T A072682 297,303,336,354,357,363,396,414,417,423,456,474,477,483,516,534,537,
%U A072682 543,576,594,597,603,636,654,657,663,696,714,717,723,756,774,777,783
%N A072682 Numbers congruent to {3, 36, 54, 57} mod 60.
%C A072682 Numbers n such that the last digit of F(n) is 2 where F(n) is the n-th Fibonacci number.
%H A072682 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A072682 Sequence contains numbers of the form: 3+60k, 36+60k, 54+60k, 57+60k, k>=0.
%F A072682 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 A072682 From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F A072682 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A072682 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 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 A072682 Select[Range[800], MemberQ[{3,36,54,57}, Mod[#,60]]&] (* _Harvey P. Dale_, Apr 07 2013 *)
%o A072682 (Magma) [n: n in [0..800] | n mod 60 in [3, 36, 54, 57]];  // _Bruno Berselli_, Jun 14 2016
%Y A072682 Cf. A000045, A002265, A003893.
%K A072682 nonn,easy
%O A072682 1,1
%A A072682 _Benoit Cloitre_, Aug 07 2002
%E A072682 Simpler definition from _Ralf Stephan_, Jun 18 2005