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%I #20 May 30 2022 03:50:23
%S 7,113,1327,1669,2477,2971,3271,4297,4831,5591,31397,34061,43331,
%T 44293,58831,155921,370261,492113,604073,1357201,1561919,2010733,
%U 2127163,2238823,4652353,6034247,7230331,8421251,8917523,11113933,20831323
%N 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.
%C 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.
%D R. K. Guy, "Unsolved Problems in Number Theory", Springer-Verlag 1994, A8, p. 21.
%D P. Ribenboim, "The Little Book of Big Primes", Springer-Verlag 1991, p. 143.
%H H. J. Smith, <a href="/A084974/b084974.txt">Table of n, a(n) for n = 1..128</a>
%H H. J. Smith, <a href="https://www.oocities.org/hjsmithh/PrimeSR/index.html">Andrica's Conjecture</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndricasConjecture.html">Andrica's Conjecture</a>.
%e 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.
%Y Cf. A078693, A079098, A079296, A084975, A084976, A084977.
%K nonn
%O 1,1
%A _Harry J. Smith_, Jun 16 2003