The Recamán Sequence
Recamán’s sequence was named after its inventor, Colombian mathematician Bernardo Recamán Santos, by Neil Sloane, creator of the On-Line Encyclopedia of Integer Sequences (OEIS). It is a well known sequence defined by a recurrence relation. In computer science they are often defined by recursion.
The Recamán Sequence is defined by-
According to this sequence first few elements are- 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224…
The sequence satisfies
MATLAB CODE FOR Recamán Sequence
n=65; % Number of Terms in the Sequence A = zeros(1,n); A(1) = 0; for ii = 1:n-1 % Algorithm to create the sequence b = A(ii)-ii; A(ii+1) = b + 2*ii; if b > 0 && ~any(A == b) A(ii + 1) = b; end end hold on; axis equal; for i = 2:1:n % Plotting the Graphs y = 0; x = (A(i)+A(i-1))/2; r = (A(i)-A(i-1))/2; th = 0:pi/50:pi; if A(i)>A(i-1) xunit = r * cos(th) + x; yunit = r * sin(th) + y; end if A(i)<A(i-1) xunit = -r * cos(th) + x; yunit = -r * sin(th) + y; end if mod(i,2) == 0 h = plot(xunit, -yunit,'k'); else h = plot(xunit, yunit,'k'); end end