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What is the law if one said the word Rishon versus Echad?
Initially one is to use the term Echad rather than Rishon when counting. Nevertheless, one who counted on the first night using the term Rishon, such as “Hayom Rishon Laomer”, fulfills his obligation. Some however suggest that the term Rishon/first is not the same as Echad/one, and one hence does not fulfill his obligation if he casually told someone “Today is the first day of the Omer”. If, however he intends to count the day using the term Rishon, then according to all he fulfills his obligation.
 Pardes Yosef Parshas Emor 13/15 in name of Divrei Shaul; Piskeiy Teshuvos 489/5
The reason: This is to negate the opinion of the Sadducees who held the first day of Sefira is on a Sunday. 
 Orchos Chaim Spinka 489/8 in name of Meoreiy Or; Piskeiy Teshuvos 489/5
 See Orchos Rabbeinu p. 112 in name of Chazon Ish that one who said to his friend that “Today is the first day of the Omer” may recount with a blessing.
 Piskeiy Teshuvos ibid footnote 21 in explanation of Chazon Ish, Upashut