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Search: id:A111064
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| A111064 |
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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. |
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1
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| 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; listen)
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OFFSET
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1,1
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EXAMPLE
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21 is the 8-th 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.
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MATHEMATICA
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fQ[n_] := Union@PrimeQ[Plus @@@ IntegerDigits[ Fibonacci@n, {2, 3, 5, 7}]] == {True}; Select[ Range[39285], fQ[ # ] &] (* Robert G. Wilson v *)
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PROGRAM
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(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;
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CROSSREFS
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Cf. A004685, A004686, A004688, A004690.
Sequence in context: A141676 A127164 A153972 this_sequence A071117 A054221 A090385
Adjacent sequences: A111061 A111062 A111063 this_sequence A111065 A111066 A111067
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KEYWORD
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nonn
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AUTHOR
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Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 12 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 14 2005
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