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A046933 Number of composites between successive primes.

%I A046933 #66 Jan 02 2024 02:41:22
%S A046933 0,1,1,3,1,3,1,3,5,1,5,3,1,3,5,5,1,5,3,1,5,3,5,7,3,1,3,1,3,13,3,5,1,9,
%T A046933 1,5,5,3,5,5,1,9,1,3,1,11,11,3,1,3,5,1,9,5,5,5,1,5,3,1,9,13,3,1,3,13,
%U A046933 5,9,1,3,5,7,5,5,3,5,7,3,7,9,1,9,1,5,3,5,7,3,1,3,11,7,3,7,3,5,11,1,17
%N A046933 Number of composites between successive primes.
%C A046933 a(n) is odd for n>1 since all primes except 2 are odd. - _Joel Brennan_, Jan 02 2023
%H A046933 T. D. Noe, <a href="/A046933/b046933.txt">Table of n, a(n) for n = 1..10000</a>
%F A046933 a(n) = prime(n+1) - prime(n) - 1 = A000040(n+1) - A000040(n) - 1.
%F A046933 a(n) = A001223(n) - 1.
%F A046933 a(n) = 2*A028334(n) - 1 for n>1. - _Giovanni Teofilatto_, Apr 19 2010
%F A046933 a(n) = Sum_{i=1..n-1} A036263(i). - _Daniel Forgues_, Apr 07 2014
%e A046933 a(1) = 0 since 2 is adjacent to 3;
%e A046933 a(2) = 1 since 4 is between 3 and 5;
%e A046933 a(4) = 3 = 11 - 7 - 1, etc.
%p A046933 A046933:=n->ithprime(n+1)-ithprime(n)-1; seq(A046933(n), n=1..100); # _Wesley Ivan Hurt_, Apr 15 2014
%t A046933 Differences[Prime[Range[100]]] - 1 (* _Arkadiusz Wesolowski_, Nov 18 2011 *)
%t A046933 Table[Prime[n + 1] - Prime[n] - 1, {n, 100}] (* _Wesley Ivan Hurt_, Apr 15 2014 *)
%t A046933 Prepend[Drop[Length/@SequenceSplit[Range@Prime@100,{_?PrimeQ}],1],0] (* _Federico Provvedi_, Jul 19 2021 *)
%o A046933 (PARI) a(n)=prime(n+1)-prime(n)-1 \\ _Charles R Greathouse IV_, Nov 20 2012
%o A046933 (Haskell)
%o A046933 a046933 n = a046933_list !! (n-1)
%o A046933 a046933_list = map (subtract 1) a001223_list
%o A046933 -- _Reinhard Zumkeller_, Dec 12 2012
%o A046933 (Python)
%o A046933 from sympy import prime
%o A046933 def A046933(n): return prime(n+1)-prime(n)-1 # _Chai Wah Wu_, Jan 02 2024
%Y A046933 Cf. A000040, A028334, A036263.
%Y A046933 Cf. A008996 (record values > 0).
%K A046933 easy,nonn,nice
%O A046933 1,4
%A A046933 _Marc LeBrun_, Dec 11 1999