|
Search: id:A112799
|
|
|
| A112799 |
|
Least odd number such that all greater odd numbers can be represented as sum of three integers with n distinct prime factors (conjectured). |
|
+0
4
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Strangely, the first 5 values of this sequence are all primes. Meng proves a remarkable generalization of the Goldbach-Vinogradov classical result that every sufficiently large odd integer N can be partitioned as the sum of three primes N = p1 + p2 + p3. The new proof is that every sufficiently large odd integer N can be partitioned as the sum of three integers N = a + b + c where each of a, b, c has k distinct prime factors for the same k.
a(5) = 95539; all odd numbers up to 200000 checked, no larger term found that could not be represented as sum of three integers each with 5 distinct prime factors.
|
|
REFERENCES
|
Xianmeng Meng, On sums of three integers with a fixed number of prime factors, Journal of Number Theory, Vol. 114 (2005), pp. 37-65.
|
|
CROSSREFS
|
Cf. A112800, A112801, A112802.
Sequence in context: A000354 A103815 A134752 this_sequence A020531 A087899 A103783
Adjacent sequences: A112796 A112797 A112798 this_sequence A112800 A112801 A112802
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 2005
|
|
|
Search completed in 0.002 seconds
|
