cp's OEIS Frontend

A096500 Let f(n) = smallest prime > n; a(n) = f(n+1) - f(n).

%I A096500 #25 Jan 29 2025 11:37:18
%S A096500 1,2,0,2,0,4,0,0,0,2,0,4,0,0,0,2,0,4,0,0,0,6,0,0,0,0,0,2,0,6,0,0,0,0,
%T A096500 0,4,0,0,0,2,0,4,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,2,0,6,0,0,0,0,0,4,0,0,
%U A096500 0,2,0,6,0,0,0,0,0,4,0,0,0,6,0,0,0,0,0,8,0,0,0,0,0,0,0,4,0,0,0,2,0,4,0,0,0
%N A096500 Let f(n) = smallest prime > n; a(n) = f(n+1) - f(n).
%H A096500 Antti Karttunen, <a href="/A096500/b096500.txt">Table of n, a(n) for n = 1..30000</a>
%H A096500 Antti Karttunen, <a href="/A096500/a096500.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A096500 From _Antti Karttunen_, Jan 03 2019: (Start)
%F A096500 a(n) = A151800(n+1) - A151800(n).
%F A096500 a(n) = A010051(1+n) * A001223(A000720(1+n)).
%F A096500 (End)
%p A096500 seq(nextprime(n+1)-nextprime(n),n=1..250); # _Muniru A Asiru_, Jan 03 2019
%t A096500 <<NumberTheory`NumberTheoryFunctions` Table[NextPrime[n+1]-NextPrime[n], {n, 1, 256}]
%t A096500 (* Second program: *)
%t A096500 Abs[Subtract @@ #] & /@ Partition[Array[NextPrime, 105], 2, 1] (* _Michael De Vlieger_, Jan 03 2019 *)
%o A096500 (PARI)
%o A096500 A151800(n) = nextprime(1+n);
%o A096500 A096500(n) = (A151800(1+n)-A151800(n)); \\ _Antti Karttunen_, Jan 03 2019
%Y A096500 Cf. A000720, A001223, A010051, A096501, A175851.
%Y A096500 First differences of A151800.
%Y A096500 Cf. also A109578.
%K A096500 nonn
%O A096500 1,2
%A A096500 _Labos Elemer_, Jul 09 2004