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%I #15 Sep 09 2021 11:51:19
%S 7,8,10,17,47,61,70,170,185,299,766,950,1247,1669,1879,2063,2090,2701,
%T 3071,5809,6190,7057,7409,8410,12754,13303,13421,14533,16250,18793,
%U 24766,24895,27370,28594,28870,29093,29189,30647,31481,36334,38123,38957
%N Numbers n such that the sum of the digits of the n-th Fibonacci number written in bases 2, 3, 5 and 7 is prime.
%e 21 is the 8th Fibonacci number. Written in bases 2,3,5,7 we obtain 10101, 210, 41 and 30. The sum of the digits of each of this representations is prime, so 8 is an element of the sequence.
%t fQ[n_] := Union@PrimeQ[Plus @@@ IntegerDigits[ Fibonacci@n, {2, 3, 5, 7}]] == {True}; Select[ Range[39285], fQ[ # ] &] (* _Robert G. Wilson v_ *)
%t Select[Range[40000],AllTrue[Total/@IntegerDigits[Fibonacci[#],{2,3,5,7}],PrimeQ]&] (* _Harvey P. Dale_, Sep 09 2021 *)
%o (MuPAD) for n from 1 to 1500 do a := numlib::fibonacci(n); if numlib::proveprime(numlib::sumOfDigits(a,2)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,3)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,5)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,7)) = TRUE then print(n); end_if; end_if; end_if; end_if; end_for;
%Y Cf. A004685, A004686, A004688, A004690.
%K nonn,base
%O 1,1
%A _Stefan Steinerberger_, Nov 12 2005
%E More terms from _Robert G. Wilson v_, Nov 14 2005
%E Corrected by _Harvey P. Dale_, Sep 09 2021
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