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A073426 Number of primes between n-th prime and n-th composite or number of primes that are >=Min[prime(n),c(n)] and are < Max[prime(n),c(n)]. 1

%I

%S 2,2,2,1,1,1,1,2,3,3,3,4,5,5,6,7,8,9,9,9,10,11,12,13,13,14,15,15,15,

%T 16,17,17,18,19,20,21,21,22,23,24,25,25,25,26,27,28,29,29,30,31,31,31,

%U 32,33,34,35,35,36,37,37,38,39,40,41,41,42,43,44,45,46,47,47,48,49,49,49

%N Number of primes between n-th prime and n-th composite or number of primes that are >=Min[prime(n),c(n)] and are < Max[prime(n),c(n)].

%F a(n)=A000720[A000040(n)]-A000720[A002808(n)], for n>=5; a(n)=A000720[A002808(n)]-n+1 for n=1, 2, 3, 4.

%e n=4: in range {p(4)=11 and c(4)=10} 1 prime was found, a(4)=1; n=25: in range {p(25)=97 and c(25)=38} 13 primes, {41,43,..,97} were found, so a(25)=13.

%t c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[PrimePi[c[w]]-w+1, {w, 1, 4}] Table[w-PrimePi[c[w]], {w, 5, 128}]

%Y Cf. A065890, A073425, A000720, A002808.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 31 2002

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Last modified March 31 14:24 EDT 2020. Contains 333151 sequences. (Running on oeis4.)