First and smallest occurrence of n, n >= 1, consecutive odd numbers that are primes or strong pseudoprime (base 2):

a(1) = 3: (3) ;

a(2) = 3: (3, 5) ;

a(3) = 3: (3, 5, 7);

a(4) = 1640293473202755797: (1640293473202755797, 1640293473202755799, 1640293473202755801, 1640293473202755803); (1640293473202755801 is strong pseudoprime base 2 and others are prime);