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%I #2 Jun 23 2014 16:31:11
%S 3,5,7,11,29,97,127,541,907,1151,1361,15727,19661,31469,156007,360749,
%T 370373,1357333,2010881,17051887,20831533,47326913,191913031,
%U 436273291,2300942869,3842611109,4302407713,10726905041,22367085353,25056082543
%N Upper ends of record prime gaps under consideration of the prime number theorem.
%C Every element > 7 must be in A000101 too (consider the derivatives of x/log(x) to prove this), but not conversely. The sequence is infinite since lim sup (length of n-th prime gap/log(n-th prime)) is infinite, proved by Westzynthius, see Ribenboim.
%D P. Ribenboim, The Book of Prime Number Records, Chapter about prime gaps.
%D E. Westzynthius, Über die Verteilung der Zahlen, die zu den n ersten Primzahlen teilerfremd sind Comm. Phys. Math. Helsingfors 25, 1931.
%F A prime p belongs to the sequence iff p/log(p) - q/log(q) attains a new high, where q is the preceding prime.
%e 541 is okay since 541/log(541) - 523/log(523) = 2.4108.. was not reached by smaller primes
%Y Cf. A060769, A000101.
%K nonn
%O 1,1
%A Ulrich Schimke (ulrschimke(AT)aol.com)