1,1

On the infinite square grid we draw a infinite straight line from the point (1,0) in direction (2,1).

We start at stage 1 from the point (0,0) drawing a edge ((0,0),(2,0)) in a horizontal direction.

At stage 2 we draw a edge ((2,0),(2,2)) in a vertical direction. We can see that the straight line intercepts to the number 3 (The first odd prime).

At stage 3 we draw a edge ((2,2),(4,2)) in a horizontal direction. We can see that the straight line intercepts to the number 5 (The second odd prime).

And so on (See illustrations).

The absolute value of a(n) is equal to the length of the n-th edge of a path, or infinite square polyedge, such that the mentioned straight line intercepts, on the path, to the number 1 and the odd primes. In other words, the straight line intercepts the odd non-composite numbers (A006005).

The position of the x-th odd non-composite number A006005(x) is represented by the point P(x,x-1) .

So, the position of the first prime number is represented by the point P(2,0) and position of the x-th prime A000040(x), for x>1, is represented by the point P(x,x-1), for example: 31, the 11-st prime, is represented by the point P(11,10).

See also A162200, A162201 and A162202 for more information.

O. E. Pol, Graph of the mountain path function for prime numbers

O. E. Pol, Illustration: The mountain path of the primes

Array begins:

=====

X..Y

=====

2, 2;

2, 3;

1,-1;

1, 3;

1,-1;

1, 3;

1,-3;

1, 4;

1,-2;

1, 5;

Cf. A000040, A006005, A008578, A162200, A162201, A162202, A162340, A162341, A162342, A162343, A162344.

Sequence in context: A004489 A112599 A106795 this_sequence A071455 A139465 A010244

Adjacent sequences: A162200 A162201 A162202 this_sequence A162204 A162205 A162206

easy,more,sign

Omar E. Pol (info(AT)polprimos.com), Jun 27 2009

Edited by Omar E. Pol (info(AT)polprimos.com), Jul 02 2009