

A103669


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


3



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
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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 A018006
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



