

A266498


Index of the smallest triangular number greater than 3^n.


0



2, 3, 4, 7, 13, 22, 38, 66, 115, 198, 344, 595, 1031, 1786, 3093, 5357, 9279, 16071, 27836, 48213, 83508, 144640, 250524, 433920, 751571, 1301759, 2254713, 3905278, 6764140, 11715834, 20292419, 35147501, 60877257, 105442502, 182631770, 316327505, 547895310, 948982514, 1643685930, 2846947542
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Also, a(n) is the largest integer m such that binomial(m,2) <= 3^n.
a(n) gives a theoretical upper bound for the number of coins such that two fake coins (of equal weight lighter than the other coins) among them can be identified in n weightings on a balance scale. It was shown that the bound is achievable for all n<=10, but it remains an open question if the bound is achievable for n>10.


LINKS



FORMULA

a(n) = round( sqrt(2*3^n+1/4) ).


PROG

(PARI) a(n) = round( sqrt(2*3^n+1/4) );


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



