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A088700
Number of primes between successive semiprimes.
9
1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0
OFFSET
1,4
COMMENTS
a(n) = 0 for almost all n. The average order of a(n) is 1/log log n. - Charles R Greathouse IV, Apr 29 2012
LINKS
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Semiprime
FORMULA
a(n) = A000720(A001358(n+1)) - A000720(A001358(n));
a(A088701(n)) = n and a(k) <> n for 1 <= k < A088701(n).
EXAMPLE
a(34)=3, as there are three primes between A001358(34)=19*5=95 and A001358(34+1)=53*2=106: 97, 101 and 103.
MATHEMATICA
Select[Range[400], PrimeOmega[#] == 2&] // PrimePi // Differences (* Jean-François Alcover, Oct 12 2021 *)
CROSSREFS
Cf. A001358, (semiprimes), A088701, A103668 (semiprimes between primes).
Cf. A214520 (primes that are the only prime between consecutive semiprimes).
Sequence in context: A039973 A035171 A352567 * A287121 A035446 A126211
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 08 2003
STATUS
approved