cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A112799 Least odd number such that all greater odd numbers can be represented as sum of three integers with n distinct prime factors (conjectured).

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%I A112799 #10 Mar 13 2019 13:06:00
%S A112799 5,29,283,4409,95539,2579897,88149143
%N A112799 Least odd number such that all greater odd numbers can be represented as sum of three integers with n distinct prime factors (conjectured).
%C A112799 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.
%C A112799 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.
%C A112799 a(1)-a(3): checked odd numbers < 10^5. a(4): checked odd numbers < 10^6. a(5): checked odd numbers < 3*10^6. a(6): checked odd numbers < 3*10^7. a(7): checked odd numbers between 8*10^7 and 2*10^8. [From _Donovan Johnson_, Feb 04 2009]
%H A112799 Xianmeng Meng, <a href="https://doi.org/10.1016/j.jnt.2005.04.013">On sums of three integers with a fixed number of prime factors</a>, Journal of Number Theory, Vol. 114 (2005), pp. 37-65.
%Y A112799 Cf. A112800, A112801, A112802.
%K A112799 nonn,more
%O A112799 1,1
%A A112799 _Jonathan Vos Post_ and _Ray Chandler_, Sep 19 2005
%E A112799 a(6)-a(7) from _Donovan Johnson_, Feb 04 2009