A213520 Least number k0 such that (prime(k+1) / prime(k))^n < 2 for all k >= k0.

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

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

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

Adjacent sequences: A213517 A213518 A213519 * A213521 A213522 A213523

Keyword

nonn

Author

T. D. Noe, Jul 11 2012

Status

approved