

A259483


Numbers n such that both n*log(2) and n*log(3) are within 1/sqrt(n) of integers.


1



1, 2, 3, 4, 7, 9, 10, 19, 20, 29, 39, 42, 52, 62, 72, 91, 101, 111, 163, 254, 264, 365, 629, 730, 994, 1095, 1359, 1460, 1724, 2089, 2454, 2819, 9076, 9441, 9806, 18517, 18882, 39488, 48929, 58370, 67811, 107299, 116740, 156228, 165669, 214598, 224039, 272968, 331338, 380267
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OFFSET

1,2


COMMENTS

For any irrational x and y there exist infinitely many positive integers n such that max(n*x  Z, n*y  Z) < 1/sqrt(n), where Z is the set of integers.


LINKS

Robert Israel and Robert G. Wilson v, Table of n, a(n) for n = 1..78


EXAMPLE

52*log(2)  41 and 52*log(3)  65 are both less than 1/sqrt(52) so 52 is in the sequence.


MAPLE

nm:= x > abs(xround(x)): f:= n > is(max(nm(n*Pi), nm(n*exp(1)))<n^(1/2)): select(f, [$1 .. 20000]);


MATHEMATICA

fQ[n_] := Abs[n*Log[2]  Round[n*Log[2]]] Sqrt[n] < 1 && Abs[n*Log[3]  Round[n*Log[3]]] Sqrt[n] < 1; Select[ Range@ 400000, fQ@ # &]


CROSSREFS

Cf. A208530.
Sequence in context: A057267 A277066 A138576 * A187503 A038197 A187506
Adjacent sequences: A259480 A259481 A259482 * A259484 A259485 A259486


KEYWORD

nonn


AUTHOR

Robert Israel and Robert G. Wilson v, Jun 28 2015


STATUS

approved



