This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A377030 #37 Jul 23 2025 16:06:10
%S A377030 0,3,6,9,7,4,1,2,5,8,8,5,2,1,4,7,9,6,3,0,3,6,9,7,4,1,2,5,8,8,5,2,1,4,
%T A377030 7,9,6,3,0,3,6,9,7,4,1,2,5,8,8,5,2,1,4,7,9,6,3,0,3,6,9,7,4,1,2,5,8,8,
%U A377030 5,2,1,4,7,9,6,3,0,3,6,9,7,4,1,2,5,8,8,5,2,1,4,7,9,6,3,0
%N A377030 Period 19: repeat [0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3].
%C A377030 Difference between the multiples of 3 (A008585) and the closest multiple of 19 (A008601). For any two numbers (in this case p=3 and q=19), a sequence is produced consisting of a palindrome cycle. If p and q are coprime, then the cycle length is equal to max(p,q). The biggest number in the sequence will be at most half of max(p,q). Here is a plot of the first cycle of this sequence:
%C A377030 9 X X
%C A377030 8 X X
%C A377030 7 X X
%C A377030 6 X X
%C A377030 5 X X
%C A377030 4 X X
%C A377030 3 X X
%C A377030 2 X X
%C A377030 1 X X
%C A377030 0 X X
%H A377030 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F A377030 a(n) = a(n-19). - _David A. Corneth_, Oct 14 2024
%F A377030 a(n) = min(3*n-19*floor(3*n/19), 19*ceil(3*n/19)-3*n).
%t A377030 LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3},96] (* _James C. McMahon_, Oct 31 2024 *)
%o A377030 (C)
%o A377030 int p = 3;
%o A377030 int q = 19;
%o A377030 for (int t = 0;t <= 99;t++) {
%o A377030 int closest = 999;
%o A377030 for (int i = 0;i <= 99;i++) {
%o A377030 int dist=abs(i * q - t * p);
%o A377030 if (dist < closest) {
%o A377030 closest = dist;
%o A377030 }
%o A377030 }
%o A377030 printf("%i, ", closest);
%o A377030 }
%o A377030 (PARI) a(n) = my(n3 = 3*n); min(n3 - 19*floor(n3/19), ceil(19*ceil(n3/19) - n3)) \\ _David A. Corneth_, Oct 14 2024
%o A377030 (Python)
%o A377030 def A377030(n): return (0, 3, 6, 9, 7, 4, 1, 2, 5, 8, 8, 5, 2, 1, 4, 7, 9, 6, 3)[n%19] # _Chai Wah Wu_, Oct 31 2024
%Y A377030 Cf. A008585, A008601.
%K A377030 nonn,easy
%O A377030 0,2
%A A377030 _Neil Vaughan_, Oct 13 2024