OFFSET
1,4
COMMENTS
The prime k-tuples conjecture implies that, for each k >= 2, each j from 1 to k-1 occurs infinitely often as T(n,n-k).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
EXAMPLE
Triangle begins:
0
1 0
2 1 0
3 1 1 0
4 3 2 1 0
5 4 3 2 1 0
For n=10 and k=7, the points to interpolate are [7, 17], [8, 19], [9, 23], [10, 29]. These are interpolated by the polynomial y = x^2 - 13*x + 59 of degree 2, so T(10,7) = 2.
MAPLE
g:= proc(n, m) local L, d;
L:= [seq(ithprime(i), i=m..n)];
for d from 0 do
L:= L[2..-1]-L[1..-2];
if L = [] or convert(L, set) = {0} then return d fi
od
end proc:
for n from 1 to 10 do
seq(g(n, m), m=1..n)
od;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Robert Israel, Jul 01 2020
STATUS
approved