A084977 Values that show the slow decrease in the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.

670873, 639281, 463722, 292684, 260522, 256245, 244265, 228429, 215476, 213675, 203053, 167894, 144069, 137748, 119533, 108882, 92024, 81248, 63042, 56651, 52808, 52185, 36338, 36089, 35698, 29717, 27520, 26189, 23440, 23096, 23005

Offset: 1

Author

Harry J. Smith, Jun 16 2003

Keywords

• nonn

Comments

a(n) = floor(1000000*Af(k)) with 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)=46372 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, A084976.