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 A084974 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. 5
 7, 113, 1327, 1669, 2477, 2971, 3271, 4297, 4831, 5591, 31397, 34061, 43331, 44293, 58831, 155921, 370261, 492113, 604073, 1357201, 1561919, 2010733, 2127163, 2238823, 4652353, 6034247, 7230331, 8421251, 8917523, 11113933, 20831323 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) are the primes p(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. 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. EXAMPLE a(3)=1327 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. CROSSREFS Cf. A078693, A079098, A079296, A084975, A084976, A084977. Sequence in context: A079296 A081531 A142537 * A156240 A152927 A064330 Adjacent sequences:  A084971 A084972 A084973 * A084975 A084976 A084977 KEYWORD nonn AUTHOR Harry J. Smith, Jun 16 2003 STATUS approved

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