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%I #10 Mar 25 2022 10:38:22
%S 1,5,10,12,12,31,31,31,31,35,35,47,48,48,63,63,67,67,67,67,100,100,
%T 100,100,100,100,100,218,218,218,218,218,218,218,218,218,218,218,218,
%U 218,218,218,218,218,218,218,218,218,264,264,264,264,264,264,264,264
%N Least number k0 such that (prime(k+1) / prime(k))^n < 2 for all k >= k0.
%C Equivalently, prime(k+1) / prime(k) < 2^(1/n). The case n = 2 is proved by Dressler et al.
%H T. D. Noe, <a href="/A213520/b213520.txt">Table of n, a(n) for n = 1..1000</a>
%H Robert E. Dressler, Louis Pigno, and Robert Young, <a href="http://www.jstor.org/stable/43774462">Sums of squares of primes</a>, Nordisk Mat. Tidskr. 24 (1976), 39-40.
%t Table[t = Table[(Prime[i+1]/Prime[i])^n, {i, 20*n}]; pos = Position[t, _?(# > 2 &)]; If[pos == {}, 1, pos[[-1,1]] + 1], {n, 60}]
%Y Cf. A213521 (prime(a(n))).
%K nonn
%O 1,2
%A _T. D. Noe_, Jul 11 2012
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