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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.
4
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
1,1
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.
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
Eric Weisstein's World of Mathematics, Andrica's Conjecture
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Harry J. Smith, Jun 16 2003
STATUS
approved