%I
%S 2,2,2,3,1,1,1,3,1,1,1,3,1,3,1,4,1,2,1,5,1,1,1,3,1,3,1,6,1,2,1,
%T 4,1,3,1,3,1,2,1,5,1,3,1,7,1,4,1,3,1,1,1,3,1,1,1,9,1,7,1,5,1,
%U 2,1,6,1,4,1,4,1,4,1,5,1,3,1,6,1,2,1,6
%N The mountain path of the primes (see comment lines for definition).
%C On the infinite square grid we draw an infinite straight line from the point (1,0) in direction (2,1).
%C We start at stage 1 from the point (0,0) drawing an edge ((0,0),(2,0)) in a horizontal direction.
%C At stage 2 we draw an edge ((2,0),(2,2)) in a vertical direction. We can see that the straight line intercepts at the number 3 (the first odd prime).
%C At stage 3 we draw an edge ((2,2),(4,2)) in a horizontal direction. We can see that the straight line intercepts at the number 5 (the second odd prime).
%C And so on (see illustrations).
%C The absolute value of a(n) is equal to the length of the nth edge of a path, or infinite square polyedge, such that the mentioned straight line intercepts, on the path, at the number 1 and the odd primes. In other words, the straight line intercepts the odd noncomposite numbers (A006005).
%C The position of the xth odd noncomposite number A006005(x) is represented by the point P(x,x1).
%C So the position of the first prime number is represented by the point P(2,0) and position of the xth prime A000040(x), for x>1, is represented by the point P(x,x1); for example, 31, the 11th prime, is represented by the point P(11,10).
%C See also A162200, A162201 and A162202 for more information.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polmpfpn.jpg"> Graph of the mountain path function for prime numbers</a>
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polmpca1.jpg"> Illustration: The mountain path of the primes</a>
%F From _Nathaniel Johnston_, May 10 2011: (Start)
%F a(2n+1) = 1 for n >= 2.
%F a(2n) = (1)^n*(A162341(n+2)  1) = (1)^n*(A052288(n)  1) + 1 for n >= 2. (End)
%e Array begins:
%e =====
%e X..Y
%e =====
%e 2, 2;
%e 2, 3;
%e 1,1;
%e 1, 3;
%e 1,1;
%e 1, 3;
%e 1,3;
%e 1, 4;
%e 1,2;
%e 1, 5;
%Y Cf. A000040, A006005, A008578, A162200, A162201, A162202, A162340, A162341, A162342, A162343, A162344.
%K easy,sign
%O 1,1
%A _Omar E. Pol_, Jun 27 2009
%E Edited by _Omar E. Pol_, Jul 02 2009
%E More terms from _Nathaniel Johnston_, May 10 2011
