OFFSET
1,1
COMMENTS
If prime_omega(n) as defined as A001222 and a set of values becomes a string, then the 'just' means that its string is not a substring of some larger string. See the example below.
Yet another way to think of this is that between any two consecutive primes there are 'just' n semiprimes with the first one being cited above.
a(91) > 1.8*10^12. - Giovanni Resta, Aug 15 2013
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..90
FORMULA
a(n) is the next semiprime after A228171(n+1).
EXAMPLE
a(1) = 9 because between 9 and 10 there are no primes;
a(2) = 33 because between 33 and 35 (the second semiprime past 33) there are no primes;
a(3) = 91 because between 91 and 95 (the third semiprime past 91 with 93 & 94 also semiprimes) there are no primes;
a(4) = 141 because between 141 and 146 (the fourth semiprime past 141 with 142, 143 & 145 also being semiprimes) there are no primes;
the reason a(4) is not 115 is because although there are no primes between 115 and 121, the string "2, 3, 3, 2, 2, 5, 2, 2" is a substring of the string generated by 115 through 123. See the next line.
a(5) = 115 because between 115 and 123 (the fifth semiprime past 115 with 118, 119, 121, and 122 also being semiprimes) there are no primes;
MATHEMATICA
NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; t = Table[0, {100}]; p=3; While[p < 3100000000, q = NextPrime[p]; a = Count[ PrimeOmega[ Range[p, q]], 2]; If[ t[[a]] == 0, t[[a]] = p; Print[{p, a}]]; p = q]; NextSemiPrime@# & /@ t
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved