

A074788


Prime numbers generated by the sequence a(n+1) = a(n1) + a(n2) with initial values a(1)=3, a(2)=0, a(3)=2.


1



2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797, 22584751787583336797527561822649328254745329
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OFFSET

1,1


COMMENTS

a(17) has 44 digits; a(18) has 114 digits; a(19) has 128 digits. [From Harvey P. Dale, Aug 11 2011]


LINKS

Table of n, a(n) for n=1..16.
Math. Forum, Discussion
Eric Weisstein's World of Mathematics, Perrin Sequence


FORMULA

a(n+1) = a(n1)+a(n2) if a(n+1) is prime and a(1) = 3, a(2) = 0, a(3) = 2


EXAMPLE

a(1)=3, a(2)=0, a(3)=2 a(n+1) = a(n1) + a(n2). For n = 3, a(4) = a(2) + a(1) = 0 + 3 = 3; n = 4, a(5) = a(3) + a(2) = 2 + 0 = 2 etc


MATHEMATICA

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 *)


PROG

(PARI) \ compute primes in the sequence a(n+1) = a(n1)+ a(n2) \ 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[x1]+a[x2]; if(isprime(a[x+1]), print("a("x+1") = "a[x+1])) ) }


CROSSREFS

Sequence in context: A178382 A030480 A048418 * A070805 A103385 A103389
Adjacent sequences: A074785 A074786 A074787 * A074789 A074790 A074791


KEYWORD

nonn


AUTHOR

Cino Hilliard, Sep 07 2002


EXTENSIONS

Edited by Robert G. Wilson v, Sep 13 2002


STATUS

approved



