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A198293 a(n) = (1/n)*A205406(n).

%I A198293 #18 Dec 07 2021 11:09:47
%S A198293 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,
%T A198293 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,
%U A198293 1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,3
%N A198293 a(n) = (1/n)*A205406(n).
%C A198293 For a guide to related sequences, see A204892.
%H A198293 Paolo Xausa, <a href="/A198293/b198293.txt">Table of n, a(n) for n = 1..20000</a>
%t A198293 (See the program at A205402.)
%t A198293 s[m_]:=s[m]=Floor[(m+1)^2/2]/2
%t A198293 A205406[n_]:=(k=2;found=False;While[!found,Do[If[Mod[d=s[k]-s[j],n]==0,found=True;Break[]],{j,k-1}];k++];d)
%t A198293 nterms=100;Table[A205406[n]/n,{n,nterms}] (* _Paolo Xausa_, Dec 03 2021 *)
%o A198293 (PARI)
%o A198293 A002620(n) = ((n^2)>>2);
%o A198293 A002620shiftedleft(n) = A002620(1+n);
%o A198293 A205406(n) = { my(d); for(k=2,oo, for(j=1,k-1,if(!((d=A002620shiftedleft(k)-A002620shiftedleft(j))%n),return(d)))); };
%o A198293 A198293(n) = (A205406(n)/n); \\ _Antti Karttunen_, Dec 03 2021
%Y A198293 Cf. A002620, A205402, A205406, A204892.
%K A198293 nonn
%O A198293 1,9
%A A198293 _Clark Kimberling_, Jan 27 2012
%E A198293 Data section extended up to a(111) by _Antti Karttunen_, Dec 03 2021