OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 30 2015
STATUS
approved