OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..30998
EXAMPLE
Consider an irregular array in which the odd-indexed rows list successive odd numbers that are not twin primes (A255763) and the even-indexed rows list successive twin primes (A001097), 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 numbers that are not twin primes (A255763) and of twin primes (A001097).
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
. |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | 31
. |_ _ _ _ _ _ _ _ _ _ _ _ _ _ | | 29
. | | | | |_ _ _ _ _ _ _ _ _ | | | 19
. | | | | |_ _ _ _ _ _ _ _ | | | | 17
. | | | | | |_ _ _ _ _ _ | | | | | 13
. | | | | | |_ _ _ _ _ | | | | | | 11
. | | | | | | |_ _ _ | | | | | | | 7
. | | | | | | |_ _ | | | | | | | | 5
. A255763 | | | | | | |_ | | | | | | | | | 3
. 1 | | | | | | |_|_|_|_| | | | | | | A001097
. 9 | | | | | |_ _ _ _ _|_|_| | | | |
. 15 | | | | |_ _ _ _ _ _ _ _|_|_| | |
. 21 | | | |_ _ _ _ _ _ _ _ _ _ _| | |
. 23 | | |_ _ _ _ _ _ _ _ _ _ _ _| | |
. 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..8:
.
. |_ _ _
. |_ _
. |_ _
. |
. |
. |
. |_ _
.
The sequence begins: 1,3,1,2,1,2,4,2,...
.
PROG
(PARI) istwin(n) = isprime(n) && (isprime(n-2) || isprime(n+2));
lista(nn) = {my(nb = 1, istp = 0); forstep (n=3, nn, 2, if (bitxor(istp, ! istwin(n)), nb++, print1(nb, ", "); nb = 1; istp = ! istp); ); } \\ Michel Marcus, May 25 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 31 2015
EXTENSIONS
More terms from Michel Marcus, May 25 2015
STATUS
approved