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%I #30 Jul 23 2015 14:39:46
%S 4,15,224,50175,2517530624,6337960442777829375,
%T 40169742574216538983356186036612890624,
%U 1613608218478824775913354216413699241125577233045500390244103887844987109375
%N a(0) = 4; a(n) = a(n-1)^2 - 1.
%C This is the next analog of A003096 with different initial value a(0), as starting with a(0) = 2 is A003096 and a(0) = 3 is A003096 with first term omitted. It alternates between even and odd values, specifically between 4 mod 10 and 5 mod 10 and is always composite (by difference of squares factorization).
%C a(n+2) is divisible by a(n)^2. A007814(a(2 n)) = A153893(n). - _Robert Israel_, Jul 20 2015
%H Robert Israel, <a href="/A139244/b139244.txt">Table of n, a(n) for n = 0..10</a>
%H A. V. Aho and N. J. A. Sloane, <a href="http://www.fq.math.ca/11-4.html">Some doubly exponential sequences</a>, The Fibonacci Quarterly, 11 (1973), 429-437.
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n-1) = ceiling(c^(2^n)) where c is a constant between 1 and 2.
%F More specifically, c=1.9668917617901763653335057202... (sequence A260315). - _Chayim Lowen_, Jul 17 2015
%p A[0]:= 4:
%p for n from 1 to 10 do A[n]:= A[n-1]^2-1 od:
%p seq(A[i],i=0..10); # _Robert Israel_, Jul 20 2015
%t a=4; lst={a}; Do[b=a^2-1; AppendTo[lst,b]; a=b, {n,10}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 28 2010 *)
%o (PARI) a(n)=if(n,a(n-1)^2-1,4) \\ _Charles R Greathouse IV_, Jul 23 2015
%Y Cf. A003096, A007814, A153893, A260315.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Jun 06 2008
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