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A213520
Least number k0 such that (prime(k+1) / prime(k))^n < 2 for all k >= k0.
3
1, 5, 10, 12, 12, 31, 31, 31, 31, 35, 35, 47, 48, 48, 63, 63, 67, 67, 67, 67, 100, 100, 100, 100, 100, 100, 100, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 218, 264, 264, 264, 264, 264, 264, 264, 264
OFFSET
1,2
COMMENTS
Equivalently, prime(k+1) / prime(k) < 2^(1/n). The case n = 2 is proved by Dressler et al.
LINKS
Robert E. Dressler, Louis Pigno, and Robert Young, Sums of squares of primes, Nordisk Mat. Tidskr. 24 (1976), 39-40.
MATHEMATICA
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}]
CROSSREFS
Cf. A213521 (prime(a(n))).
Sequence in context: A271922 A271920 A329773 * A241145 A050680 A293726
KEYWORD
nonn
AUTHOR
T. D. Noe, Jul 11 2012
STATUS
approved