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Index of Fibonacci and tribonacci numbers having the same last digit.
3

%I #16 Aug 09 2020 12:39:41

%S 1,2,4,5,8,10,13,19,31,44,47,61,73,80,88,101,104,106,115,119,122,145,

%T 160,166,178,181,188,209,214,232,233,235,244,257,260,262,271,272,281,

%U 304,308,317,320,326,392,401,407,409,415,418,422,425,442,443,448,449

%N Index of Fibonacci and tribonacci numbers having the same last digit.

%C Fib[a(n)]=Trib[a(n)] mod 10.

%C All corresponding values of Fib and Trib (mod 10) are odd.

%H Harvey P. Dale, <a href="/A186077/b186077.txt">Table of n, a(n) for n = 1..1000</a>

%e a(10)=44 since Fib(44)=701408733 and Trib(44)=104479306403 both have 3 as last digit.

%t Module[{nn=450,f,t},f=Mod[Fibonacci[Range[nn]],10];t=Mod[ LinearRecurrence[ {1,1,1},{1,1,1},nn],10];Position[Thread[{f,t}],_?(#[[1]] == #[[2]]&),1,Heads-> False]]//Flatten (* _Harvey P. Dale_, Aug 09 2020 *)

%Y Cf. A000045.

%K nonn,base

%O 1,2

%A _Carmine Suriano_, Feb 11 2011