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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, 28594, 28870, 29093, 29189, 30647, 31481, 36334, 38123, 38957 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..41.

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 *)

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

Cf. A004685, A004686, A004688, A004690.

Sequence in context: A127164 A153972 A286420 * A071117 A054221 A195240

Adjacent sequences:  A111061 A111062 A111063 * A111065 A111066 A111067

KEYWORD

nonn,base

AUTHOR

Stefan Steinerberger, Nov 12 2005

EXTENSIONS

More terms from Robert G. Wilson v, Nov 14 2005

STATUS

approved

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Last modified June 19 05:27 EDT 2019. Contains 324218 sequences. (Running on oeis4.)