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A205406 a(n) = s(k)-s(j), where (k,j) is the least pair for which n divides s(k)-s(j), and s(j) = floor((j+1)^2/2)/2.

%I A205406 #18 Dec 07 2021 13:08:38
%S A205406 1,2,3,4,5,6,7,8,18,10,11,12,13,14,15,16,34,18,19,20,21,22,23,24,50,
%T A205406 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U A205406 98,50,51,52,106,54,55,56,57,58,59,60,61,62,63,64,65,66,201,68
%N A205406 a(n) = s(k)-s(j), where (k,j) is the least pair for which n divides s(k)-s(j), and s(j) = floor((j+1)^2/2)/2.
%C A205406 For a guide to related sequences, see A204892.
%H A205406 Antti Karttunen, <a href="/A205406/b205406.txt">Table of n, a(n) for n = 1..12004</a>
%F A205406 a(n) = n * A198293(n). - _Antti Karttunen_, Dec 05 2021
%e A205406 The least k such that 9 divides s(k)-s(j) for some k is k=8, for which j=2: s(8)-s(2) = 20-2 = 18, so a(9)=18.
%t A205406 (See the program at A205402.)
%t A205406 s[m_]:=s[m]=Floor[(m+1)^2/2]/2
%t A205406 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 A205406 nterms=100; Table[A205406[n], {n, nterms}] (* _Paolo Xausa_, Dec 03 2021 *)
%o A205406 (PARI)
%o A205406 A002620(n) = ((n^2)>>2);
%o A205406 A002620shiftedleft(n) = A002620(1+n);
%o A205406 A205406(n) = { my(d); for(k=2,oo, for(j=1,k-1,if(!((d=A002620shiftedleft(k)-A002620shiftedleft(j))%n),return(d)))); }; \\ _Antti Karttunen_, Dec 05 2021
%Y A205406 Cf. A002620, A198293, A205402, A204892.
%K A205406 nonn,look
%O A205406 1,2
%A A205406 _Clark Kimberling_, Jan 27 2012
%E A205406 Definition corrected by _Clark Kimberling_, Dec 05 2021