A248891 Number of primes p such that p+2 is prime and A001359(n) < p < A001359(n)^(1+1/n).

1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 3, 4, 3, 3, 2, 1, 2, 3, 2, 2, 5, 4, 3, 2, 1, 1, 4, 3, 2, 3, 4, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 6, 9, 8, 8, 7, 7, 7, 8, 7, 6, 6, 5, 4, 3, 3, 3, 2, 7, 6, 5, 5, 5, 4, 3, 2, 5, 5, 8, 9, 11, 10, 10, 9, 9, 8, 7, 7, 6, 6, 6, 5, 4, 5, 8, 8

Offset: 1

Author

Jahangeer Kholdi and Farideh Firoozbakht, Nov 22 2014

Keywords

• nonn

Comments

Conjecture: For every positive integer n, A001359(n+1)^(1/(n+1)) < A001359(n)^(1/n). Note that this conjecture is equivalent to " A001359 is infinite and for every n, A001359(n+1) < A001359(n)^(1+1/n). This implies for every n, a(n) is positive. See comment lines of the sequence A001359.

Examples

			Take n=1, A001359(1)=3, 3 < 5 < 3^(1+1/1)=9 hence a(1)=1.
Take n=6, A001359(6)=41, 41 < 59 < 71 < 41^(1+1/6)~76.13 hence a(6)=2.
		

Crossrefs

Cf. A001359, A248901, A248902, A248903.