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A256253
Number of successive odd nonprimes A014076 and number of successive odd primes A065091, interleaved.
3
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.
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 30 2015
STATUS
approved