login
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.
0
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
1,1
EXAMPLE
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.
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 *)
PROG
(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;
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Nov 14 2005
Corrected by Harvey P. Dale, Sep 09 2021
STATUS
approved