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 A218585 Number of ways to write n as x+y with 0
 0, 1, 1, 1, 1, 1, 2, 0, 3, 1, 2, 1, 3, 2, 3, 2, 2, 1, 4, 1, 4, 3, 4, 2, 3, 3, 3, 3, 5, 2, 6, 2, 4, 4, 5, 3, 5, 2, 8, 4, 4, 4, 7, 3, 5, 2, 8, 4, 7, 2, 8, 4, 7, 5, 7, 4, 7, 3, 8, 4, 9, 3, 11, 4, 8, 5, 10, 4, 9, 5, 9, 6, 8, 5, 6, 6, 10, 5, 10, 3, 12, 7, 10, 6, 8, 6, 11, 4, 7, 4, 15, 8, 13, 6, 9, 5, 15, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Conjecture: a(n)>0 for all n>1 with the only exception n=8. Note that any prime p=1(mod 3) can be written uniquely in the form x(p)^2+x(p)y(p)+y(p)^2 with x(p)>y(p)>0. Zhi-Wei Sun also conjectured that (sum_{p12. - Zak Seidov_, Sep 25 2013 REFERENCES Thomas Ordowski, Personal e-mail messages, Oct. 3-4, 2012, and Nov. 3, 2012. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..20000 Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv preprint arXiv:1211.1588, 2012. EXAMPLE For n=20 we have a(20)=1 since x^2+x(20-x)+(20-x)^2 with 0

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)