
COMMENTS

a(6) > 10^11.
If the ktuple conjecture is true then a(n) always exists. Weak upper bounds are
a(7) <= 105629504093565907896809
a(8) <= 9921941384213872059341198331469403
a(9) <= 376847848512740851019714299079899219399
a(10) <= 32108207632017215023964871615662539298039357


EXAMPLE

Trivially, primes 2, 3, and 5 are consecutive squarefree numbers so a(1)a(3) are each 2.
4058471, 4058473, 4058477, and 4058479 are the least 4 primes that are also consecutive squarefree numbers (4058472 = 2^3*3*11*15373, 4058474 = 2*7^2*41413, 4058475 = 3*5^2*53*1021, 4058476 = 2^2*19*53401, and 4058478 = 2*3^3*17*4421) so a(4) = 4058471.
