A256252 Number of successive odd noncomposite numbers A006005 and number of successive odd composite numbers A071904, interleaved.

4, 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

1,1

Comments

See also A256253 and A256262 which contain similar diagrams.

Links

Table of n, a(n) for n=1..104.

Formula

a(n) = A256253(n+1), n >= 2.

Example

Consider an irregular array in which the odd-indexed rows list successive odd noncomposite numbers (A006005) and the even-indexed rows list successive odd composite numbers (A071904), 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 noncomposite numbers A006005 and odd composite numbers A071904:
.            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
.           |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |   31
.           |_ _ _ _ _ _ _ _ _ _ _ _ _ _  | |   29
.           | | |_ _ _ _ _ _ _ _ _ _ _  | | |   23
.           | | | |_ _ _ _ _ _ _ _ _  | | | |   19
.           | | | |_ _ _ _ _ _ _ _  | | | | |   17
.           | | | | |_ _ _ _ _ _  | | | | | |   13
.           | | | | |_ _ _ _ _  | | | | | | |   11
.           | | | | | |_ _ _  | | | | | | | |    7
.           | | | | | |_ _  | | | | | | | | |    5
.           | | | | | |_  | | | | | | | | | |    3
.   A071904 | | | | | |_|_|_|_| | | | | | | |    1
.      9    | | | | |_ _ _ _ _|_|_| | | | | | A006005
.     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..9:
.                      _ _ _ _
.                             |_ _
.                                 |_ _
.                                     |_
.                                       |
.                                       |_ _
.
The sequence begins:      4,1,2,1,2,1,1,2,2,...
.

Prog

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

Crossrefs

Cf. A005408, A006005, A071904, A256253, A256262.

Sequence in context: A153094 A144870 A370211 * A247004 A010640 A244424

Adjacent sequences: A256249 A256250 A256251 * A256253 A256254 A256255

Keyword

nonn

Author

Omar E. Pol, Mar 30 2015

Status

approved