A211007 -id:A211007 - cp's OEIS frontend

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

Omar E. Pol, Aug 11 2012

nonn

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

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

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

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

1 together with A162154.

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

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

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

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

A211006 Pair (n,p) where n is the sum of adjacent nonprimes and p is the sum of adjacent primes.

Original entry on oeis.org

1, 5, 4, 5, 6, 7, 27, 11, 12, 13, 45, 17, 18, 19, 63, 23, 130, 29, 30, 31, 170, 37, 117, 41, 42, 43, 135, 47, 250, 53, 280, 59, 60, 61, 320, 67, 207, 71, 72, 73, 380, 79, 243, 83, 430, 89, 651, 97, 297, 101, 102, 103, 315, 107, 108, 109, 333, 113, 1560, 127, 387, 131

Offset: 1

Omar E. Pol, Aug 11 2012

			-----------------------------------------
.     Array from
n      A000027                      a(n)
-----------------------------------------
1         1;                          1
2         2, 3;                       5
3         4;                          4
4         5;                          5
5         6;                          6
6         7;                          7
7         8, 9, 10;                  27
8        11;                         11
9        12;                         12
10       13;                         13
11       14, 15, 16;                 45
12       17;                         17
13       18;                         18
14       19;                         19
15       20, 21, 22;                 63
16       23;                         23
17       24, 25, 26, 27, 28;        130

Partial sums give A211007.
A variant of A109921.
Cf. A000040, A018252, A054265, A211005.

a(n) = A109921(n+2), n >= 3.

cp's OEIS Frontend

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

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