This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A228170 The least semiprime (A001358) such that between it and the next n semiprimes, but not the next n+1 semiprimes, there are no primes. 2
 9, 33, 91, 141, 115, 213, 1382, 1639, 1133, 2558, 2973, 1329, 15685, 16143, 9974, 35678, 34063, 43333, 19613, 107381, 162145, 44294, 404599, 461722, 838259, 155923, 535403, 492117, 396737, 2181739, 370262, 1468279, 6034249, 3933601, 1671783, 25180174, 1357203 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001358, A133478, A112888, A228171. Sequence in context: A005939 A020326 A201024 * A112888 A048479 A031880 Adjacent sequences:  A228167 A228168 A228169 * A228171 A228172 A228173 KEYWORD nonn AUTHOR Jack Brennen, Jonathan Vos Post, Zak Seidov, and Robert G. Wilson v, Aug 14 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 01:59 EST 2019. Contains 329850 sequences. (Running on oeis4.)