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

%I A211005 #36 Feb 10 2023 16:09:20
%S A211005 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,
%T A211005 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,
%U A211005 1,1,5,1,5,1,3,1,5,1,5,1,1,1,9,1,1,1
%N A211005 Pair (i, j) where i = number of adjacent nonprimes and j = number of adjacent primes.
%C A211005 Also number of consecutive occurrences of n-1 in A069754. - _Reinhard Zumkeller_, Dec 04 2012
%C A211005 Run lengths of A010051. - _Paolo Xausa_, Jan 17 2023
%H A211005 Reinhard Zumkeller, <a href="/A211005/b211005.txt">Table of n, a(n) for n = 1..10000</a>
%F A211005 a(n) = A162154(n-1), n >= 2.
%e A211005 ----------------------------------------------------------
%e A211005 .     Array from              Number of   Number of
%e A211005 n      A000027                nonprimes    primes    a(n)
%e A211005 ----------------------------------------------------------
%e A211005 1         1;                      1          0        1
%e A211005 2         2, 3;                   0          2        2
%e A211005 3         4;                      1          0        1
%e A211005 4         5;                      0          1        1
%e A211005 5         6;                      1          0        1
%e A211005 6         7;                      0          1        1
%e A211005 7         8, 9, 10;               3          0        3
%e A211005 8        11;                      0          1        1
%e A211005 9        12;                      1          0        1
%e A211005 10       13;                      0          1        1
%e A211005 11       14, 15, 16;              3          0        3
%e A211005 12       17;                      0          1        1
%e A211005 13       18;                      1          0        1
%e A211005 14       19;                      0          1        1
%e A211005 15       20, 21, 22;              3          0        3
%e A211005 16       23;                      0          1        1
%e A211005 17       24, 25, 26, 27, 28;      5          0        5
%e A211005 18       29;                      0          1        1
%e A211005 19       30;                      1          0        1
%e A211005 20       31;                      0          1        1
%t A211005 A211005[upto_]:=Map[Length, Most[Split[PrimeQ[Range[upto]]]]];
%t A211005 A211005[500] (* _Paolo Xausa_, Jan 17 2023 *)
%o A211005 (Haskell)
%o A211005 import Data.List (group)
%o A211005 a211005 n = a211005_list !! (n-1)
%o A211005 a211005_list = map length $ group a069754_list
%o A211005 -- _Reinhard Zumkeller_, Dec 04 2012
%Y A211005 1 together with A162154.
%Y A211005 Cf. A000040, A001223, A010051, A018252, A046933, A211006, A211007.
%K A211005 nonn
%O A211005 1,2
%A A211005 _Omar E. Pol_, Aug 11 2012