

A078607


Least positive integer x such that 2*x^n>(x+1)^n.


4



1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 102
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..71.


FORMULA

a(n) = ceiling(1/(2^(1/n)1)). For most n, a(n) is the nearest integer to n/log(2), but there are exceptions, including n=777451915729368.


EXAMPLE

a(2)=3 as 2^2=4, 3^2=9 and 4^2=16.
For n=777451915729368, a(n) = 1121626023352384 = ceiling(n log 2), where n*log(2) = 1121626023352383.5  2.13*10^17 and 2*floor(n log 2)^n / floor(1 + n log 2)^n = 1  3.2*10^32.  M. F. Hasler, Nov 02 2013


MATHEMATICA

Table[SelectFirst[Range@ 120, 2 #^n > (# + 1)^n &], {n, 0, 71}] (* Michael De Vlieger, May 01 2016, Version 10 *)


PROG

(PARI) for (n=2, 50, x=2; while (2*x^n<=((x+1)^n), x++); print1(x", "))


CROSSREFS

Cf. A078608, A078609. Equals A110882(n)1 for n > 0.
Sequence in context: A175320 A001953 A230748 * A292043 A292052 A187484
Adjacent sequences: A078604 A078605 A078606 * A078608 A078609 A078610


KEYWORD

nonn


AUTHOR

Jon Perry, Dec 09 2002


EXTENSIONS

Edited by Dean Hickerson, Dec 17 2002
Initial terms a(0)=1 and a(1)=2 added by M. F. Hasler, Nov 02 2013


STATUS

approved



