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A129745
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Numbers n such that Lucas(4n)/7 is prime.
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0
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5, 17, 19, 41, 43, 71, 1511, 2339, 3469, 4787, 7211, 9781
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| L(k) = Lucas(k) = Fibonacci(k-1) + Fibonacci(k+1). 7 = L(4). 7 divides L(4(1+2k)). L(4n) = L(4)*L(4(n-1)) - L(4(n-2)). Conjecture: All terms are primes.
Integer n is in this sequence iff n is prime and 4n belongs to A085726. [From Max Alekseyev (maxale(AT)gmail.com), May 16 2010]
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MATHEMATICA
| a=7; b=47; Do[ c=7b-a; a=b; b=c; If[ PrimeQ[c/7], Print[n] ], {n, 3, 100}]
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CROSSREFS
| Cf. A000032, A001606 = Indices of prime Lucas numbers. Cf. A074304 = numbers n such that Lucas(2n)/3 is prime.
Sequence in context: A140568 A019349 A124873 * A038964 A019401 A153320
Adjacent sequences: A129742 A129743 A129744 * A129746 A129747 A129748
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KEYWORD
| less,more,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), May 14 2007, May 16 2007
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EXTENSIONS
| a(7) - a(10) from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 17 2007
a(11) from Max Alekseyev (maxale(AT)gmail.com), Nov 25 2007
a(12) from Alexander Adamchuk (alex(AT)kolmogorov.com), May 15 2010
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