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