A267122 Numbers n such that 1.5^n is closer to an integer than 1.5^m for any 0 < m < n.

1, 2, 4, 29, 46, 58, 95, 153, 157, 163, 455, 1060, 1256, 2677, 3328, 12429, 49304, 112896, 129638, 164000

Offset

1,2

Comments

Zudilin proves that the distance from 1.5^n to the nearest integer is at least 0.5803^n for large enough n; it seems that n > 4 suffices. (The "large enough" constant in the proof is effective but not explicit.)

Links

Table of n, a(n) for n=1..20.

Wadim Zudilin, A new lower bound for ∥(3/2)^k∥, J. Théor. Nombres Bordeaux 19:1 (2007), pp. 311-323.

Example

1.5^29 = 127834.039... which is within 0.039... of an integer, yielding a(4) = 29.
1.5^46 = 125949925.968... which is within 0.031... of an integer, yielding a(5) = 46.

Prog

(PARI) f(x)=x=frac(x); if(x>1/2, 1-x, x)
t=r=1; for(n=1, 1e6, tt=f(t*=3/2); if(tt<r, r=tt; print1(n", ")))

Crossrefs

Cf. A079490, A080052.

Sequence in context: A126580 A329063 A124687 * A018291 A033167 A081464

Adjacent sequences: A267119 A267120 A267121 * A267123 A267124 A267125

Keyword

nonn

Author

Charles R Greathouse IV, Jan 11 2016

Status

approved