A103669 First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.

1, 2, 4, 11, 24, 34, 30, 47, 221, 259, 189, 375, 429, 217, 1831, 1879, 1229, 3795, 3644, 4522, 2225, 10229, 14862, 4612, 34202, 38590, 66762, 14357, 44227, 40933, 33608, 161441, 31545, 111924, 415069, 278832, 126172, 1576499, 104071, 271743, 786922, 3183065, 4875380, 3166684, 2219883, 6080675, 6443469, 1319945

Offset

1,2

Comments

k(31)>78496, k(32)=31545.

The first occurrence of k in A103668. - Robert G. Wilson v, May 07 2005

Links

Table of n, a(n) for n=1..48.

Example

n=3, k=11, p(11)=31, p(12)=37, three semiprimes between 31 and 37 are 33=3*11, 34=2*17,35=5*7.

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; f[n_] := Count[fQ /@ Range[Prime[n] + 1, Prime[n + 1] - 1], True];
t = Table[ f[n], {n, 1600000}]; Position[t, #, 1, 1] & /@ Range[0, 41] // Flatten (* Or *) t = Table[0, {50}]; Do[ a = f[n]; If[ t[[a + 1]] == 0, t[[a + 1]] = n], {n, 1600000}]

Crossrefs

Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700, number of semiprimes between two successive primes: A103668.

Cf. A000040, A088700, A001358, A103654, A103655, A103668.

Sequence in context: A298926 A292157 A256801 * A230711 A034485 A362042

Adjacent sequences: A103666 A103667 A103668 * A103670 A103671 A103672

Keyword

base,nonn

Author

Zak Seidov, Feb 12 2005

Extensions

More terms from Robert G. Wilson v, May 07 2005

Status

approved