A205406 - OEIS

%I #18 Dec 07 2021 13:08:38

%S 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 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,

%U 98,50,51,52,106,54,55,56,57,58,59,60,61,62,63,64,65,66,201,68

%N 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 For a guide to related sequences, see A204892.

%H Antti Karttunen, <a href="/A205406/b205406.txt">Table of n, a(n) for n = 1..12004</a>

%F a(n) = n * A198293(n). - _Antti Karttunen_, Dec 05 2021

%e 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 (See the program at A205402.)

%t s[m_]:=s[m]=Floor[(m+1)^2/2]/2

%t 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 nterms=100; Table[A205406[n], {n, nterms}] (* _Paolo Xausa_, Dec 03 2021 *)

%o (PARI)

%o A002620(n) = ((n^2)>>2);

%o A002620shiftedleft(n) = A002620(1+n);

%o 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 Cf. A002620, A198293, A205402, A204892.

%K nonn,look

%O 1,2

%A _Clark Kimberling_, Jan 27 2012

%E Definition corrected by _Clark Kimberling_, Dec 05 2021