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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: A228405 A276824 A235998 * 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

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Last modified February 21 14:29 EST 2018. Contains 299414 sequences. (Running on oeis4.)