A084976 Values of k 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.

4, 30, 217, 263, 367, 429, 462, 590, 650, 738, 3385, 3644, 4522, 4612, 5949, 14357, 31545, 40933, 49414, 104071, 118505, 149689, 157680, 165326, 325852, 415069, 491237, 566214, 597311, 733588, 1319945, 1736516, 2850174, 2857960, 3183065

Offset: 1

Author

Harry J. Smith, Jun 16 2003

Keywords

• nonn

Comments

a(n) are values of k 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)=217 because p(217)=1327, p(218)=1361 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
• H. J. Smith, Andrica's Conjecture
• Eric Weisstein's World of Mathematics, Andrica's conjecture.

Crossrefs

Cf. A078693, A079098, A079296, A084974, A084975, A084977.