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Indices of Fibonacci numbers whose last digit is 5.
2

%I #28 Jan 01 2022 09:55:42

%S 5,10,20,25,35,40,50,55,65,70,80,85,95,100,110,115,125,130,140,145,

%T 155,160,170,175,185,190,200,205,215,220,230,235,245,250,260,265,275,

%U 280,290,295,305,310,320,325,335,340,350,355,365,370,380

%N Indices of Fibonacci numbers whose last digit is 5.

%C Sequence contains numbers of the forms 5 + 60*k, 10 + 60*k, 20 + 60*k, 25 + 60*k, 35 + 60*k, 40 + 60*k, 50 + 60*k, 55 + 60*k, where k>=0.

%C Numbers that are congruent to {5, 10, 20, 25} mod 30. - _Amiram Eldar_, Jan 01 2022

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 15*(n-1)-a(n-1), with a(1)=5. - _Vincenzo Librandi_, Aug 08 2010

%F a(1)=5, a(2)=10, a(3)=20, a(n)=a(n-1)+a(n-2)-a(n-3). - Harvey P. Dale, May 15 2011

%F a(n) = -(5/4)*(3+(-1)^n-6*n). - _Harvey P. Dale_, May 15 2011

%F G.f.: 5*x*(x^2+x+1) / ((x-1)^2*(x+1)). - _Colin Barker_, Jun 16 2013

%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(15*sqrt(3)) = A248897 / 10. - _Amiram Eldar_, Jan 01 2022

%t Flatten[Position[Fibonacci[Range[400]],_?(Last[IntegerDigits[#]]==5&)]] (* or *) LinearRecurrence[{1,1,-1},{5,10,20},60] (* or *) Table[-(5/4) (3+(-1)^n-6 n),{n,60}] (* _Harvey P. Dale_, May 15 2011 *)

%Y Cf. A000045, A003893, A248897.

%K nonn,base,easy

%O 1,1

%A _Benoit Cloitre_, Aug 07 2002

%E Edited by _M. F. Hasler_, Oct 08 2014