A211005 Pair (i, j) where i = number of adjacent nonprimes and j = number of adjacent primes.

1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 3, 1, 5, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 5, 1, 3, 1, 5, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 13, 1, 3, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 5, 1, 3, 1, 5, 1, 5, 1, 1, 1, 9, 1, 1, 1

Offset: 1

Author

Omar E. Pol, Aug 11 2012

Keywords

• nonn

Comments

Also number of consecutive occurrences of n-1 in A069754. - Reinhard Zumkeller, Dec 04 2012

Run lengths of A010051. - Paolo Xausa, Jan 17 2023

Examples

			----------------------------------------------------------
.     Array from              Number of   Number of
n      A000027                nonprimes    primes    a(n)
----------------------------------------------------------
1         1;                      1          0        1
2         2, 3;                   0          2        2
3         4;                      1          0        1
4         5;                      0          1        1
5         6;                      1          0        1
6         7;                      0          1        1
7         8, 9, 10;               3          0        3
8        11;                      0          1        1
9        12;                      1          0        1
10       13;                      0          1        1
11       14, 15, 16;              3          0        3
12       17;                      0          1        1
13       18;                      1          0        1
14       19;                      0          1        1
15       20, 21, 22;              3          0        3
16       23;                      0          1        1
17       24, 25, 26, 27, 28;      5          0        5
18       29;                      0          1        1
19       30;                      1          0        1
20       31;                      0          1        1
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

1 together with A162154.

Cf. A000040, A001223, A010051, A018252, A046933, A211006, A211007.

Programs

Haskell

import Data.List (group)
a211005 n = a211005_list !! (n-1)
a211005_list = map length $ group a069754_list
-- Reinhard Zumkeller, Dec 04 2012

Mathematica

A211005[upto_]:=Map[Length, Most[Split[PrimeQ[Range[upto]]]]];
A211005[500] (* Paolo Xausa, Jan 17 2023 *)

Formula

a(n) = A162154(n-1), n >= 2.