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A074788 Prime numbers in the Perrin sequence b(n+1) = b(n-1) + b(n-2) with initial values b(1)=3, b(2)=0, b(3)=2.

%I A074788 #31 Feb 16 2025 08:32:47
%S A074788 2,3,5,7,17,29,277,367,853,14197,43721,1442968193,792606555396977,
%T A074788 187278659180417234321,66241160488780141071579864797,
%U A074788 22584751787583336797527561822649328254745329
%N A074788 Prime numbers in the Perrin sequence b(n+1) = b(n-1) + b(n-2) with initial values b(1)=3, b(2)=0, b(3)=2.
%C A074788 a(17) has 44 digits; a(18) has 114 digits; a(19) has 128 digits. - _Harvey P. Dale_, Aug 11 2011
%H A074788 Michael De Vlieger, <a href="/A074788/b074788.txt">Table of n, a(n) for n = 1..24</a>
%H A074788 Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H A074788 Math. Forum, <a href="http://www.mathforum.org/discuss/sci.math/">Discussion</a>
%H A074788 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerrinSequence.html">Perrin Sequence</a>
%F A074788 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
%e A074788 a(1)=3, a(2)=0, a(3)=2; then for n = 3, a(4) = a(2) + a(1) = 0 + 3 = 3; for n = 4, a(5) = a(3) + a(2) = 2 + 0 = 2 etc
%t A074788 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}]
%t A074788 Union[Select[LinearRecurrence[{0,1,1},{3,0,2},500],PrimeQ]] (* _Harvey P. Dale_, Aug 11 2011 *)
%o A074788 (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])) )
%Y A074788 Cf. A112881, A001608.
%K A074788 nonn
%O A074788 1,1
%A A074788 _Cino Hilliard_, Sep 07 2002
%E A074788 Edited by _Robert G. Wilson v_, Sep 13 2002