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Starting from a(1)=1, a(n) is the minimum integer greater than a(n-1) such that a(n)+a(n-1), a(n)*a(n-1)+1 and a(n)*a(n-1)-1 are all primes.
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%I #6 Aug 27 2013 09:30:50

%S 1,4,15,16,27,74,375,398,465,482,945,962,1149,1228,1485,1624,1737,

%T 1820,1941,1990,2031,2690,2787,3040,3327,3436,3525,3704,3855,3934,

%U 4383,4484,4515,4712,6375,6592,7239,7322,7545,7616,7935,8138,9381,9518,11445,11594

%N Starting from a(1)=1, a(n) is the minimum integer greater than a(n-1) such that a(n)+a(n-1), a(n)*a(n-1)+1 and a(n)*a(n-1)-1 are all primes.

%C Terms are alternately odd and even.

%H Paolo P. Lava, <a href="/A228590/b228590.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4)=16 and 27 is the minimum integer greater than 16 such that 16+27=43, 16*27-1=431, 16*27+1=433 are all primes.

%p with(numtheory); P:=proc(q) local a, b, n; a:=1; b:=0; print(a);

%p for n from 1 to q do while not isprime(a+b) and not isprime (a*b+1) and not isprime (a*b-1) do

%p b:=b+2; od; print(b); a:=b; b:=b+1; od; print(); end: P(10^4);

%Y Cf. A228588, A228589.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Aug 27 2013