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 A268131 If a(n) is not squarefree, then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier. 1

%I

%S 1,2,3,4,7,5,6,8,14,9,23,10,11,12,23,13,15,16,31,17,18,35,19,20,39,21,

%T 22,24,46,25,71,26,27,53,28,81,109,29,30,32,62,33,34,36,70,37,38,40,

%U 78,41,42,43,44,87,45,132,177,47,48,95,49,144,193,50,243

%N If a(n) is not squarefree, 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 squarefree numbers. In contrast to that sequence we have many "lines" here (when the property occurs for consecutive terms), roughly proportional to n, 2n, 3n, ... Here we also have duplicate terms (which we could exclude explicitly), for n <= 1000 this happens 19 times.

%H M. F. Hasler, <a href="/A268131/b268131.txt">Table of n, a(n) for n = 1..1000</a>

%o (PARI) {a(n,show=0,is=x->issquarefree(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]),L+1,a[#a]+a[#a-1])));if(type(show)=="t_VEC",a,a[#a])}

%K nonn,look

%O 1,2

%A _M. F. Hasler_, Jan 26 2016

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)