|
|
A344120
|
|
For n >= 0, let N = 243 + n*343, let v(x) be the maximum power of 7 dividing x, and let p(N) be the partition function A000041(N). If v(p(N)) >= v(24*N-1) then a(n)=1, otherwise a(n)=0.
|
|
2
|
|
|
0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0
|
|
COMMENTS
|
For n == 2,4, or 5 mod 7, a(n) = 1 [K. G. Ramanathan, p. 149, Corollary 1].
For n == 0,1,3, or 6 mod 7, it appears that a(n) = 0 in about 80% of the cases.
|
|
LINKS
|
|
|
EXAMPLE
|
a(0) = 0 because N = 243, p(243) = 133978259344888 = 2^3 * 7^2 * 97 * 5783 * 609289, so v(p(N)) = 2. Also 24*243 - 1 = 7^3 * 17, and v(24*N-1) = 3.
|
|
PROG
|
(PARI) a(n) = my(N = 243 + n*343); (n%7==2)||(n%7==4)||(n%7==5) || valuation(numbpart(N), 7) >= valuation(24*N-1, 7);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|