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%I #15 Aug 28 2019 08:16:24
%S 2,2,2,2,2,3,3,2,3,3,3,4,4,3,4,4,5,5,5,5,4,5,5,7,6,6,5,5,5,5,7,7,7,7,
%T 8,7,8,9,8,8,7,7,9,8,9,8,9,11,10,10,11,10,10,9,10,11,10,9,9,9,8,10,11,
%U 11,10,11,12,12,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,14,15,14,13
%N Number of primes in the interval [prime(n),n+prime(n)].
%F a(n) = Pi(n+prime(n)) - n + 1 = A000720(n+A000040(n)) - n + 1. [corrected by _Michel Marcus_, Aug 28 2019]
%t t[x_] := Table[w, {w, Prime[x], x+Prime[x]}] Table[Count[PrimeQ[t[n]], True], {n, 1, 128}] (* or *) Table[PrimePi[n+Prime[n]]-n+1, {n, 1, 25}];
%o (PARI) a(n) = primepi(n+prime(n)) - n + 1; \\ _Michel Marcus_, Aug 28 2019
%Y Cf. A000040, A000720, A061067, A061068, A084295.
%K nonn
%O 1,1
%A _Labos Elemer_, May 27 2003
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