A256262 Number of successive odd numbers that are not twin primes and number of successive twin primes, interleaved.

1, 3, 1, 2, 1, 2, 4, 2, 4, 2, 7, 2, 4, 2, 13, 2, 1, 2, 13, 2, 4, 2, 13, 2, 4, 2, 1, 2, 13, 2, 4, 2, 13, 2, 4, 2, 13, 2, 16, 2, 34, 2, 4, 2, 13, 2, 28, 2, 22, 2, 13, 2, 7, 2, 10, 2, 7, 2, 73, 2, 4, 2, 1, 2, 13, 2, 10, 2, 67, 2, 4, 2, 7, 2, 4, 2, 13, 2, 28, 2

Offset: 1

Author

Omar E. Pol, Mar 31 2015

Keywords

• nonn

Comments

See also both A256252 and A256253 which contain similar diagrams.

Examples

			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,...
.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30998

Crossrefs

Cf. A005408, A001097, A256252, A256253, A255763.

Programs

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

Extensions

More terms from Michel Marcus, May 25 2015