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A074788
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Prime numbers generated by the sequence a(n+1) = a(n-1) + a(n-2) with initial values a(1)=3, a(2)=0, a(3)=2.
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1
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2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797, 22584751787583336797527561822649328254745329
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OFFSET
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1,1
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COMMENTS
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a(17) has 44 digits; a(18) has 114 digits; a(19) has 128 digits. [From Harvey P. Dale, Aug 11 2011]
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LINKS
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Table of n, a(n) for n=1..16.
Math. Forum, Discussion
Eric Weisstein's World of Mathematics, Perrin Sequence
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).
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FORMULA
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a(n+1) = a(n-1)+a(n-2) if a(n+1) is prime and a(1) = 3, a(2) = 0, a(3) = 2
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EXAMPLE
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a(1)=3, a(2)=0, a(3)=2 a(n+1) = a(n-1) + a(n-2). For n = 3, a(4) = a(2) + a(1) = 0 + 3 = 3; n = 4, a(5) = a(3) + a(2) = 2 + 0 = 2 etc
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MATHEMATICA
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a[1] = 3; a[2] = 0; a[3] = 2; a[n_] := a[n] = a[n - 2] + a[n - 3]; Do[ If[ PrimeQ[ a[n]], Print[ a[n]]], {n, 1, 357}]
Union[Select[LinearRecurrence[{0, 1, 1}, {3, 0, 2}, 500], PrimeQ]] (* Harvey P. Dale, Aug 11 2011 *)
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PROG
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(PARI) \ compute primes in the sequence a(n+1) = a(n-1)+ a(n-2) \ a(1)=3; a(2)=0: a(3)=2. a(0) not allowed in PARI aprime(n) = { a=vector(n+1); a[1]=3; a[2]=0; a[3]=2; print("n a(n+1)"); for(x=3, n, a[x+1]=a[x-1]+a[x-2]; if(isprime(a[x+1]), print("a("x+1") = "a[x+1])) ) }
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CROSSREFS
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Sequence in context: A178382 A030480 A048418 * A262833 A070805 A255161
Adjacent sequences: A074785 A074786 A074787 * A074789 A074790 A074791
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard, Sep 07 2002
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EXTENSIONS
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Edited by Robert G. Wilson v, Sep 13 2002
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STATUS
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approved
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