A065554 Numbers k such that floor((3/2)^(k+1))/floor((3/2)^k) = 3/2.

2, 9, 11, 13, 24, 29, 31, 36, 37, 40, 41, 43, 49, 50, 51, 67, 68, 70, 72, 73, 77, 79, 80, 86, 88, 91, 92, 95, 101, 102, 103, 115, 121, 126, 127, 132, 134, 136, 142, 145, 146, 151, 154, 156, 162, 165, 167, 171, 172, 176, 178, 179, 181, 191, 193, 194, 195, 198, 199

Offset: 1

Author

Benoit Cloitre, Nov 28 2001

Keywords

• nonn

Comments

Also k such that A002380(k+1) = 3*A002380(k). - Benoit Cloitre, Apr 21 2003

It appears that lim_{n->oo} a(n)/n = 3. - Benoit Cloitre, Jan 29 2006

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002379, A002380.

Programs

Mathematica

a[1] = 2; a[n_ ] := a[n] = Block[ {k = a[n - 1] + 1}, While[ Floor[(3/2)^(k + 1)] / Floor[(3/2)^k] != 3/2, k++ ]; Return[k]]; Table[ a[n], {n, 1, 70} ]

PARI

isok(k) = { my(f=3/2); floor(f^(k+1))/floor(f^k) == f } \\ Harry J. Smith, Oct 22 2009

Extensions

More terms from Robert G. Wilson v, Nov 30 2001