A111064 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.
7, 8, 10, 17, 47, 61, 70, 170, 185, 299, 766, 950, 1247, 1669, 1879, 2063, 2090, 2701, 3071, 5809, 6190, 7057, 7409, 8410, 12754, 13303, 13421, 14533, 16250, 18793, 24766, 24895, 27370, 28594, 28870, 29093, 29189, 30647, 31481, 36334, 38123, 38957
Offset: 1
Examples
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.
Programs
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Mathematica
fQ[n_] := Union@PrimeQ[Plus @@@ IntegerDigits[ Fibonacci@n, {2, 3, 5, 7}]] == {True}; Select[ Range[39285], fQ[ # ] &] (* Robert G. Wilson v *) Select[Range[40000],AllTrue[Total/@IntegerDigits[Fibonacci[#],{2,3,5,7}],PrimeQ]&] (* Harvey P. Dale, Sep 09 2021 *) -
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;
Extensions
More terms from Robert G. Wilson v, Nov 14 2005
Corrected by Harvey P. Dale, Sep 09 2021