A084975 Primes that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.

11, 127, 1361, 1693, 2503, 2999, 3299, 4327, 4861, 5623, 31469, 34123, 43391, 44351, 58889, 156007, 370373, 492227, 604171, 1357333, 1562051, 2010881, 2127269, 2238931, 4652507, 6034393, 7230479, 8421403, 8917663, 11114087, 20831533

Offset: 1

Author

Harry J. Smith, Jun 16 2003

Keywords

• nonn

Comments

a(n) are the primes p(k+1) such that Af(k) > Af(m) for all m > k. This sequence relies on a heuristic calculation and there is no proof that it is correct.

Examples

			a(3)=1361 because p(218)=1361, p(217)=1327 and Af(217) = sqrt(1361) - sqrt(1327) = 0.463722... is larger than any value of Af(m) for m>217.
		

References

• R. K. Guy, "Unsolved Problems in Number Theory", Springer-Verlag 1994, A8, p. 21.
• P. Ribenboim, "The Little Book of Big Primes", Springer-Verlag 1991, p. 143.

Links

• H. J. Smith, Table of n, a(n) for n=1..128
• Eric Weisstein's World of Mathematics, Andrica's Conjecture
• H. J. Smith, Andrica's Conjecture

Crossrefs

Cf. A078693, A079098, A079296, A084974, A084976, A084977.