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a(1) = 2, a(n+1) is the largest squarefree number < 2*a(n).
2

%I #14 May 13 2024 16:16:12

%S 2,3,5,7,13,23,43,85,167,331,661,1321,2641,5281,10561,21121,42241,

%T 84481,168961,337921,675841,1351681,2703361,5406721,10813441,21626881,

%U 43253761,86507521,173015041,346030081,692060161,1384120321,2768240641

%N a(1) = 2, a(n+1) is the largest squarefree number < 2*a(n).

%C Analogous to Bertrand's primes.

%H Hugo Pfoertner, <a href="/A076994/b076994.txt">Table of n, a(n) for n = 1..360</a>

%p with(numtheory):a[1] := 2:for n from 2 to 84 do q := 2*a[n-1]-1:while(not issqrfree(q)) do q := q-1:od:a[n] := q:od:seq(a[l],l=1..84);

%t lsfn[n_]:=Module[{s=2n-1},While[!SquareFreeQ[s],s--];s]; NestList[ lsfn,2,40] (* _Harvey P. Dale_, Nov 28 2018 *)

%Y Cf. A006992, A076995.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Oct 26 2002

%E More terms from _Sascha Kurz_, Jan 26 2003