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%I #18 Jul 23 2014 15:10:21
%S 1,2,3,5,8,13,21,34,13,47,60,107,167,274,441,167,608,775,167,942,1109,
%T 2051,3160,1109,4269,5378,1109,6487,7596,1109,8705,9814,1109,10923,
%U 12032,1109,13141,14250,1109,15359,16468,31827,15359,47186,62545,15359,77904,93263,171167,264430
%N A recurrence relation conditioned on the primality of the preceding terms.
%C This is like the Fibonacci sequence but subtraction replaces addition when neither of the preceding two terms are prime numbers.
%H Paul Tek, <a href="/A236768/b236768.txt">Table of n, a(n) for n = 0..1000</a>
%F a(0) = 1, a(1) = 2, a(n) = a(n-1) + a(n-2) unless both a(n-1) and a(n-2) are composite, then a(n) = a(n-1) - a(n-2).
%e a(6) = 21 because a(5)=13 is prime and 13 + 8 = 21.
%e a(7) = 34 because a(5) is prime and 21 + 13 = 34.
%e a(8) = 13 because neither a(6) nor a(7) is prime and 34 - 21 = 13.
%t modFibo[0] := 1; modFibo[1] := 2; modFibo[n_] := modFibo[n] = modFibo[n - 1] + (-1)^(Boole[Not[PrimeQ[modFibo[n - 1]] || PrimeQ[modFibo[n - 2]]]])modFibo[n - 2]; Table[modFibo[n], {n, 0, 49}] (* _Alonso del Arte_, Jan 31 2014 *)
%K nonn,easy
%O 0,2
%A _Stephen McDonald_, Jan 30 2014