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%I #18 Aug 22 2023 08:00:28
%S 1,3,15,17,233,291,577,723,1455,3615,8117,8835,9505,30833,128773,
%T 130827,239595,273435,426891,654135,676297,926117,1455533,1662533,
%U 2389517,2762427,2820927,7994449,8098527,14319073,16766835,20506733,27606617,31627817,43558023,55566015
%N Starting with a(0) = 1, smallest squarefree number k such that, for all a(m), m < n, k + a(m) is not squarefree.
%e 17 belongs to this sequence as 17 + 1, 17 + 3, 17 + 15 all are divisible by some square.
%t a[0] = 1; a[n_] := a[n] = Module[{t = Array[a, n, 0], k = a[n - 1] + 1}, While[! SquareFreeQ[k] || AnyTrue[t, SquareFreeQ[k + #] &], k++]; k]; Array[a, 20, 0] (* _Amiram Eldar_, Aug 21 2023 *)
%o (PARI) v=vector(60); v[1]=1; print1("1,");for(n=2,60, for(k=1,10^15,if(issquarefree(k),s=0;for(l=1,n-1,if(issquarefree(k+v[l]),break);s=s+1)); if(s==n-1,print1(k",");v[n]=k;break)))
%Y Cf. A013929, A077224, A080793, A085902.
%K nonn
%O 0,2
%A _Amarnath Murthy_, Nov 03 2002
%E Edited by _Ralf Stephan_, Mar 25 2003
%E More terms from _Sam Alexander_, Dec 12 2003
%E a(22) corrected and a(33)-a(35) added by _Amiram Eldar_, Aug 21 2023