This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A133850 Number of partitions of n into two primes and a semiprime. 1
 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 5, 3, 5, 3, 6, 7, 8, 4, 8, 6, 10, 8, 10, 7, 14, 10, 16, 12, 14, 9, 16, 14, 17, 12, 17, 16, 25, 15, 20, 20, 23, 20, 25, 20, 28, 22, 25, 23, 30, 23, 31, 28, 33, 28, 35, 32, 36, 30, 33, 32, 44, 35, 34, 37, 42, 43, 49, 39, 42, 42, 44, 49, 49, 40, 45, 51 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS This was inspired by the fact that our universe seems to be 73% Dark Energy, 23% Dark Matter and 4% ordinary matter, where 73 is prime, 23 is prime, 4 is semiprime. REFERENCES Guy Gugliotta, "Mining for Dark Matter", Discover, May 2007, 36-41. "Dark energy makes up 73 percent of the universe, dark matter another 23 percent. Atomic matter -- everything around us and everything astronomers have ever seen -- accounts for just 4 percent." LINKS Alois P. Heinz, Table of n, a(n) for n = 1..5000 EXAMPLE Examples: n a(n) 0-7 0 8 1 2+2+4, 9 1 2+3+4, 10 2 2+2+6 = 3+3+4, 11 2 2+3+6 = 2+5+4, 12 2 3+3+6 = 3+5+4, 13 3 2+2+9 = 2+5+6 = 2+7+4, 14 5 2+2+10 = 2+3+9 = 3+5+6 = 3+7+4 = 5+5+4, 15 3 2+3+10 = 2+7+6 = 3+3+9, 16 5 2+5+9 = 3+3+10 = 3+7+6 = 5+5+6 = 5+7+4, 17 3 2+5+10 = 2+11+4 = 3+5+9, 18 6 2+2+14 = 2+7+9 = 3+5+10 = 3+11+4 = 5+7+6 = 7+7+4, etc. MATHEMATICA semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; f[n_] := Block[{c = 0, i = j = 1, p = PrimePi[(n - 4)/2]}, While[i < p + 1, j = i; q = PrimePi[n - 4 - Prime@i]; While[j < q + 1, If[semiPrimeQ[n - Prime@i - Prime@j], c++ ]; j++ ]; i++ ]; c]; Array[f, 70] (* Robert G. Wilson v *) CROSSREFS Cf. A000040, A001358, A000002. Sequence in context: A276824 A235998 A303949 * A160902 A082408 A270566 Adjacent sequences:  A133847 A133848 A133849 * A133851 A133852 A133853 KEYWORD nonn AUTHOR Jonathan Vos Post, Jan 21 2008 EXTENSIONS More terms from Robert G. Wilson v, Jan 21 2008 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 June 25 04:18 EDT 2019. Contains 324346 sequences. (Running on oeis4.)