A256253 Number of successive odd nonprimes A014076 and number of successive odd primes A065091, interleaved.

1, 3, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 2, 1, 1, 6, 1, 1, 1, 2, 2, 4, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 4, 2, 1, 2, 5, 1, 5, 1, 1, 2, 1, 1, 2, 2, 4, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 4, 1, 6, 1, 1, 2, 1, 1, 6, 1, 2, 1, 4, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2

Offset

1,2

Comments

See also A256252 and A256262 which contain similar diagrams.

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = A256252(n-1), n >= 3.

Example

Consider an irregular array in which the odd-indexed rows list successive odd nonprimes (A014076) and the even-indexed rows list successive odd primes (A065091), in the sequence of odd numbers (A005408), as shown below:
1;
3, 5, 7;
9;
11, 13;
15;
17; 19;
21,
23;
25, 27;
39, 31;
...
a(n) is the length of the n-th row.
.
Illustration of the first 16 regions of the diagram of the symmetric representation of odd nonprimes (A014076) and of odd primes (A065091):
.            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
.           |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |   31
.           |_ _ _ _ _ _ _ _ _ _ _ _ _ _  | |   29
.           | | |_ _ _ _ _ _ _ _ _ _ _  | | |   23
.           | | | |_ _ _ _ _ _ _ _ _  | | | |   19
.           | | | |_ _ _ _ _ _ _ _  | | | | |   17
.           | | | | |_ _ _ _ _ _  | | | | | |   13
.           | | | | |_ _ _ _ _  | | | | | | |   11
.           | | | | | |_ _ _  | | | | | | | |    7
.           | | | | | |_ _  | | | | | | | | |    5
.   A014076 | | | | | |_  | | | | | | | | | |    3
.      1    | | | | | |_|_|_|_| | | | | | | | A065091
.      9    | | | | |_ _ _ _ _|_|_| | | | | |
.     15    | | | |_ _ _ _ _ _ _ _|_|_| | | |
.     21    | | |_ _ _ _ _ _ _ _ _ _ _|_| | |
.     25    | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
.     27    |_ _ _ _ _ _ _ _ _ _ _ _ _ _|_|_|
.
a(n) is also the length of the n-th boundary segment in the zig-zag path of the above diagram, between the two types of numbers, as shown below for n = 1..10:
.
.                       |_ _ _
.                             |_ _
.                                 |_ _
.                                     |_
.                                       |
.                                       |_ _
.
The sequence begins:    1,3,1,2,1,2,1,1,2,2,...
.

Prog

(PARI) lista(nn) = {my(nb = 1, isp = 0); forstep (n=3, nn, 2, if (bitxor(isp, ! isprime(n)), nb++, print1(nb, ", "); nb = 1; isp = ! isp); ); } \\ Michel Marcus, May 25 2015

Crossrefs

Cf. A005408, A014076, A047846, A065091, A175632, A251092, A256252, A256134, A256262.

Sequence in context: A212305 A205555 A165913 * A288818 A319658 A276988

Adjacent sequences: A256250 A256251 A256252 * A256254 A256255 A256256

Keyword

nonn

Author

Omar E. Pol, Mar 30 2015

Status

approved