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

1,2

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

Links

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

Formula

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

Example

----------------------------------------------------------
.     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

Mathematica

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

Prog

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

Crossrefs

1 together with A162154.

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

Sequence in context: A063669 A306489 A319734 * A162154 A134505 A329376

Adjacent sequences: A211002 A211003 A211004 * A211006 A211007 A211008

Keyword

nonn

Author

Omar E. Pol, Aug 11 2012

Status

approved