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.
Original entry on oeis.org
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
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.
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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 *)
Select[Range[40000],AllTrue[Total/@IntegerDigits[Fibonacci[#],{2,3,5,7}],PrimeQ]&] (* Harvey P. Dale, Sep 09 2021 *)
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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;
A180280
Fibonacci numbers written in base 2, read as decimal numbers which then are prime.
Original entry on oeis.org
11, 101, 1011001, 100010100101111, 1100110010100000101000011101110110101011001011001101111101101011010101110010101, 1101011110011100100011101000011100001010001101001011001100110100000011001101101001010011011001100101010111
Offset: 1
a(1) = 11 because 3 is the 4th Fibonacci number, 3 (base 2) = 11, and 11 (base 10) is prime.
a(2) = 101 because 5 is the 5th Fibonacci number, 5 (base 2) = 101, and 101 (base 10) is prime.
a(3) = 1011001 because 89 is the 11th Fibonacci number, 89 (base 2) = 1011001, and 1011001 (base 10) is prime.
a(4) = 100010100101111 because 17711 is the 22nd Fibonacci number, 17711 (base 2) = 100010100101111, and 100010100101111 (base 10) is prime.
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Select[FromDigits[IntegerDigits[#,2]]&/@Fibonacci[Range[1000]],PrimeQ] (* Harvey P. Dale, Sep 04 2024 *)
A233524
Numbers n such that the binary expansion of Fibonacci(n) is a palindrome (leading zero digits are not permitted).
Original entry on oeis.org
0, 1, 2, 4, 5, 8
Offset: 1
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t = {}; Do[b = IntegerDigits[Fibonacci[n], 2]; If[b == Reverse[b], AppendTo[t, n]], {n, 0, 1000}]; t (* T. D. Noe, Dec 14 2013 *)
Select[Range[0,10],PalindromeQ[IntegerDigits[Fibonacci[#],2]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 04 2019 *)
A280105
a(n) = prime(Fibonacci(n)) written in base 2.
Original entry on oeis.org
10, 10, 11, 101, 1011, 10011, 101001, 1001001, 10001011, 100000001, 111001101, 1100111011, 10110111111, 101000011111, 1000110001101, 1111001110001, 11010010011101, 101101001110111, 1001101101100011, 10000100101011011, 11100010001110111, 110000000001001111
Offset: 1
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[Seqint(Intseq(NthPrime(Fibonacci(n)), 2)): n in [1..25]];
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Table[FromDigits[IntegerDigits[Prime[Fibonacci[n]], 2]], {n, 1, 30}]
A287015
Lucas numbers written in base 2.
Original entry on oeis.org
10, 1, 11, 100, 111, 1011, 10010, 11101, 101111, 1001100, 1111011, 11000111, 101000010, 1000001001, 1101001011, 10101010100, 100010011111, 110111110011, 1011010010010, 10010010000101, 11101100010111, 101111110011100, 1001101010110011, 1111101001001111
Offset: 0
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[Seqint(Intseq(Lucas(n), 2)): n in [0..30]];
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Table[FromDigits[IntegerDigits[LucasL[n], 2]], {n, 0, 30}]
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