A246471 First of the least n primes that are also consecutive terms of A005117 (squarefree numbers).

2, 2, 2, 4058471, 462807341

Offset: 1

Author

Hans Havermann, Aug 27 2014

Keywords

• nonn
• hard
• more

Comments

a(6) > 10^11.

a(6) <= 10211143417747. - Jens Kruse Andersen, Sep 09 2014

If the k-tuple conjecture is true then a(n) always exists. Weak upper bounds are

a(7) <= 105629504093565907896809

a(8) <= 9921941384213872059341198331469403

a(9) <= 376847848512740851019714299079899219399

a(10) <= 32108207632017215023964871615662539298039357

- Jens Kruse Andersen, Sep 10 2014

Examples

			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.
		

Crossrefs

Cf. A005117; a(3) is first term in A242621; a(4) is first term in A246470; a(5) is first term in A246548.