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%I #13 May 21 2018 15:45:33
%S 2,3,5,7,9,10,11,12,13,19,21,23,26,28,30,39,41,46,50,51,53,55,57,59,
%T 77,89,93,101,113,129,149,151,153,161,165,178,185,189,201,221,237,245,
%U 246,297,364,377,489,553,581,639
%N Numbers m with A304720(m) = 1.
%C Conjecture: The sequence only has 112 terms as listed in the b-file.
%C We have verified that there is no new term below 2*10^9.
%H Zhi-Wei Sun, <a href="/A304721/b304721.txt">Table of n, a(n) for n = 1..112</a>
%H Zhi-Wei Sun, <a href="http://maths.nju.edu.cn/~zwsun/116f.pdf">Mixed sums of primes and other terms</a>, in: D. Chudnovsky and G. Chudnovsky (eds.), Additive Number Theory, Springer, New York, 2010, pp. 341-353.
%H Zhi-Wei Sun, <a href="https://doi.org/10.1007/978-3-319-68032-3_20">Conjectures on representations involving primes</a>, in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II, Springer Proc. in Math. & Stat., Vol. 220, Springer, Cham, 2017, pp. 279-310. (See also <a href="http://arxiv.org/abs/1211.1588">arXiv:1211.1588 [math.NT]</a>, 2012-2017.)
%e a(9) = 13 since 13 - (4^1 - 1) = 2*5 is squarefree, 13 - (4^0 - 0) = 2^2*3 is not squarefree, and 13 - (4^k -k ) < 0 for any integer k > 1.
%t f[n_]:=f[n]=4^n-n;
%t tab={};Do[r=0;k=0;Label[bb];If[f[k]>=m,Goto[aa]];If[SquareFreeQ[m-f[k]],r=r+1];If[r>1,Goto[cc]];k=k+1;Goto[bb];Label[aa];If[r==1,tab=Append[tab,m]];Label[cc],{m,1,640}];Print[tab]
%Y Cf. A000302, A005117, A024037, A304034, A304081, A304331, A304333, A304522, A304523, A304689, A304720.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, May 17 2018
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