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Integers m such that the last digit of Fibonacci(m) is 9.
1

%I #20 Mar 27 2024 12:29:40

%S 11,29,31,32,38,49,52,58,71,89,91,92,98,109,112,118,131,149,151,152,

%T 158,169,172,178,191,209,211,212,218,229,232,238,251,269,271,272,278,

%U 289,292,298,311,329,331,332,338,349,352,358,371,389,391,392,398,409

%N Integers m such that the last digit of Fibonacci(m) is 9.

%C Sequence contains numbers of form (11+60k), (29+60k), (31+60k), (32+60k), (38+60k), (49+60k), (52+60k), (58+60k), with k>=0.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F G.f.: x*(2*x^8+6*x^7+3*x^6+11*x^5+6*x^4+x^3+2*x^2+18*x+11) / (x^9-x^8-x+1). - _Colin Barker_, Jun 16 2013

%t Select[Range[500],Last[IntegerDigits[Fibonacci[#]]]==9&] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,1,-1},{11,29,31,32,38,49,52,58,71},60] (* _Harvey P. Dale_, Sep 06 2015 *)

%Y Cf. A000045, A003893.

%K nonn,base,easy

%O 1,1

%A _Benoit Cloitre_, Aug 07 2002