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%I #10 Nov 08 2016 20:54:49
%S 1,2,3,5,8,13,21,34,55,89,144,4,6,10,16,7,23,30,53,83,136,219,355,574,
%T 929,1503,2432,3935,6367,10302,16669,26971,43640,70611,114251,184862,
%U 299113,483975,783088,1267063,2050151,3317214,5367365,8684579,14051944,22736523,36788467,59524990,96313457,155838447,252151904
%N If a(n) is not a square, then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier.
%C A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for nonsquares. The sequence starts like the Fibonacci sequence up to 144, then restarts with 4 up to 16, then it restarts from 7 and grows very large.
%H M. F. Hasler, <a href="/A268133/b268133.txt">Table of n, a(n) for n = 1..100</a>
%F Empirical g.f.: (1+x-229*x^11-142*x^12-19*x^15) / (1-x-x^2). - _Colin Barker_, Jan 27 2016
%o (PARI) {a(n,show=0,is=x->issquare(x),a=[1],L=0,U=[])->while(#a<n,show&&if(type(show)=="t_STR",write(show,#a," ",a[#a]),print1(a[#a]","));if(a[#a]>L+1,U=setunion(U,[a[#a]]),L++;while(#U&&U[1]<=L+1,U=U[^1];L++));a=concat(a,if(is(a[#a])||#a<2,L+1,a[#a]+a[#a-1])));if(type(show)=="t_VEC",a,a[#a])}
%K nonn
%O 1,2
%A _M. F. Hasler_, Jan 26 2016
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