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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See also A256252 and A256262 which contain similar diagrams.

LINKS

Table of n, a(n) for n=1..105.

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

CROSSREFS

Cf. A005408, A014076, A047846, A065091, A175632, A251092, A256252, A256134, A256262.

Sequence in context: A212305 A205555 A165913 * A288818 A319658 A276988

Adjacent sequences:  A256250 A256251 A256252 * A256254 A256255 A256256

KEYWORD

nonn

AUTHOR

Omar E. Pol, Mar 30 2015

STATUS

approved

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Last modified October 19 21:08 EDT 2019. Contains 328228 sequences. (Running on oeis4.)