cp's OEIS Frontend

A268133 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.

%I A268133 #10 Nov 08 2016 20:54:49
%S A268133 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 A268133 929,1503,2432,3935,6367,10302,16669,26971,43640,70611,114251,184862,
%U A268133 299113,483975,783088,1267063,2050151,3317214,5367365,8684579,14051944,22736523,36788467,59524990,96313457,155838447,252151904
%N A268133 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 A268133 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 A268133 M. F. Hasler, <a href="/A268133/b268133.txt">Table of n, a(n) for n = 1..100</a>
%F A268133 Empirical g.f.: (1+x-229*x^11-142*x^12-19*x^15) / (1-x-x^2). - _Colin Barker_, Jan 27 2016
%o A268133 (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 A268133 nonn
%O A268133 1,2
%A A268133 _M. F. Hasler_, Jan 26 2016