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A103389 Primes in A103379.

%I A103389 #42 Sep 01 2024 02:33:02
%S A103389 2,3,5,7,17,31,71,127,157,227,257,293,349,419,503,8179,65657,68053,
%T A103389 72421,80429,258949,493109,16399511,33609887,34225183,1387603957,
%U A103389 5575987679,15932884421,35689079297,693128029907,957136790429,1129233918343,10363690074667,41632551979939,10815125582078291
%N A103389 Primes in A103379.
%F A103389 Intersection of A103379 and A000040.
%e A103389 A103379(20) = 3, which is prime, hence 3 is in this sequence.
%p A103389 A103379 := proc(n) option remember ; if n <= 12 then 1; else procname(n-11)+procname(n-12) ; fi; end: isA103379 := proc(n) option remember ; local i ; for i from 1 do if A103379(i) = n then RETURN(true) ; elif A103379(i) > n then RETURN(false) ; fi; od: end: A103389 := proc(n) option remember ; local a; if n = 1 then 2; else for a from procname(n-1)+1 do if isprime(a) then if isA103379(a) then RETURN(a) ; fi; fi; od: fi; end: for n from 1 to 37 do printf("%d, ",A103389(n)) ; od: # _R. J. Mathar_, Aug 30 2008
%t A103389 Clear[a]; k11; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103389=Union[Select[Array[a, 1000], PrimeQ]] N[Solve[x^12 - x - 1 == 0, x], 111][[2]] (* Program, edit and extension by _Ray Chandler_ and _Robert G. Wilson v_, irrelevant code deleted by _M. F. Hasler_, Sep 19 2015 *)
%t A103389 Select[LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,1,1},{1,1,1,1,1,1,1,1,1,1,1,1},700],PrimeQ]//Union (* _Harvey P. Dale_, Apr 22 2016 *)
%o A103389 (PARI) {a=vector(m=12,n,1);L=0;for(n=m,10^5,isprime(a[i=n%m+1]+=a[(n+1)%m+1])&&L<a[i]&&print1(L=a[i],","))} \\ _M. F. Hasler_, Sep 19 2015
%Y A103389 Cf. A103379, A103399.
%K A103389 easy,nonn
%O A103389 1,1
%A A103389 _Jonathan Vos Post_, Feb 15 2005
%E A103389 Corrected from a(16) on by _R. J. Mathar_, Aug 30 2008
%E A103389 Edited and more terms added by _M. F. Hasler_, Sep 19 2015