

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
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OFFSET

1,2


COMMENTS

Equivalently, prime(k+1) / prime(k) < 2^(1/n). The case n = 2 is proved by Dressler et al.


REFERENCES

Robert E. Dressler, Louis Pigno and Robert Young, Sums of squares of primes, Nordisk Mat. Tidskr. 24 (1976), 3940.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


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
Adjacent sequences: A213517 A213518 A213519 * A213521 A213522 A213523


KEYWORD

nonn


AUTHOR

T. D. Noe, Jul 11 2012


STATUS

approved



