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%I #19 Mar 31 2024 12:27:00
%S 1,13,61,73,97,217,349,649,937,1477,1513,1729,2005,2077,2209,3265,
%T 3649,3889,4093,4609,4945,5497,5749,5929,6109,7309,7441,8041,8389,
%U 8821,9925,10525,10669,11605,13201,13345,16021,18529,18649,20293,21481,22573,22729,24169
%N Numbers n such that the digit sum of Fibonacci(n) is equal to the digit sum of Lucas(n).
%C Numbers n such that A004090(n) = A139374(n).
%C Subsequence of A017533.
%C It seems that n is odd. The primes of the sequence are: 13, 61, 73, 97, 349, 937, 3889, 4093, 5749, 7309, 8389, 8821, 21481, 22573, 24169, ...
%C Fibonacci(j) == Lucas(j) (mod 9) iff j == 1 (mod 12), so all a(n) == 1 (mod 12). - _Robert Israel_, Jul 10 2014
%H Vincenzo Librandi, <a href="/A244923/b244923.txt">Table of n, a(n) for n = 1..95</a>
%e 13 is in the sequence because Fibonacci(13) = 233, Lucas(13) = 521 and 2+3+3 = 5+2+1 = 8.
%t lst={}; Table[If[Total[IntegerDigits[LucasL[n]]] == Total[IntegerDigits[Fibonacci[n]]], AppendTo[lst, n]], {n, 0, 25000}]; lst
%t Select[Range[25000],Total[IntegerDigits[Fibonacci[#]]]==Total[IntegerDigits[LucasL[#]]]&] (* _Harvey P. Dale_, Mar 31 2024 *)
%Y Cf. A000032, A000045, A004090, A017533, A139374.
%K nonn,base
%O 1,2
%A _Michel Lagneau_, Jul 08 2014