N.Y. Suffolk County Tax Act § 45
If the owner, mortgagee or occupant of or party in interest in such real estate does not pay such tax or assessment, with the costs, additions and charges, within the period stated in such advertisement, then the county treasurer shall, without further notice, commence the sale of lands specified in such notice of sale on the day set for that purpose and continue the sale from day to day until every such lot or parcel is sold. Such lands shall be sold for an amount sufficient to pay all the taxes and assessments due thereon for the years for the taxes of which said sale shall be made with interest thereon to the time of sale, and all costs, expenses and charges accrued thereon and, subject to reductions as herein provided, said amount paid for such property shall carry and bear the maximum interest and penalties as follows: six per centum on the purchase price, if redeemed within six months of date of sale. An additional six per centum on the purchase price if redeemed after the expiration of six months and within twelve months of the date of sale. An additional six per centum on the purchase price if redeemed after the expiration of twelve months and within a period of eighteen months of date of sale. An additional six per centum on the purchase price if redeemed after the expiration of eighteen months and within a period of twenty-four months of date of sale. An additional six per centum on the purchase price if redeemed after the expiration of twenty-four months and within a period of thirty months of date of sale. An additional six per centum on the purchase price if redeemed after the expiration of thirty months and within thirty-six months of date of sale. The rate of interest at which any person or persons shall offer to take the lot or parcel of land to be sold shall be established by his bid. The rate thus established shall be the rate of interest for every period of six months or fraction thereof up to the time of the redemption of the property purchased until the expiration of three years, plus all taxes paid by the purchaser with interest thereon at six per centum per annum to the date of payment. At such sale, rates of interest shall be bid in multiples of one per centum or a flat bid of no interest whatsoever and parcels shall be sold and bid upon separately. If more than one person bids the same rate of interest, the county treasurer or person conducting such sale shall sell the parcel to whichever of such bidders as he in his sole discretion shall determine. In any case, however, and as to any parcel, the county may reject any and all bids and bid in and purchase the same for the county at a rate of interest as shall be established by resolution of the county legislature, but not to exceed the maximum rate of interest as herein provided in which event the bid of the county shall be preferred over all other bids. The county shall likewise be deemed the purchaser at the rate of interest as herein provided for of all parcels which are not sold at sale. The county legislature may by resolution exclude from such sale such parcels as it determines where the county has entered into any agreement concerning the disposition of tax liens thereon with a tax district or other person pursuant to section one hundred sixty-six-a of the tax law or other provisions of law. The foregoing rates of interest shall be applied whenever those rates are greater than the rates of interest as established in section thirteen-c of this tax act.
N.Y. Suffolk County Tax Act § 45