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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 (list; graph; refs; listen; history; text; internal format)
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), 39-40.

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

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Last modified November 29 04:08 EST 2021. Contains 349416 sequences. (Running on oeis4.)