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.

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

Offset: 1

Author

Cino Hilliard, Sep 07 2002

Keywords

• nonn

Comments

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

Examples

			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
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..24
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• Math. Forum, Discussion
• Eric Weisstein's World of Mathematics, Perrin Sequence

Crossrefs

Cf. A112881, A001608.

Programs

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 *)

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])) )

Formula

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

Extensions

Edited by Robert G. Wilson v, Sep 13 2002