|
| |
|
|
A083128
|
|
Least 3-brilliant number of size n.
|
|
3
|
|
|
|
8, 12, 105, 1331, 10013, 100181, 1030301, 10000127, 100000727, 1027243729, 10000002797, 100000000757, 1002101470343, 10000000000493, 100000000005643, 1000090002700027, 10000000000001251, 100000000000000649
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Brilliant numbers, as defined by Peter Wallrodt, are numbers with two prime factors of the same length (in decimal notation). These numbers are generally used for cryptographic purposes and for testing the performance of prime factoring programs.
a(3n+1) will always be the cube of the least prime greater than 10^n.
2-brilliant numbers are A078972. 3-brilliant numbers addressed in A083128 and A083182. The sum of all 1, 2 and 3-digit 2-brilliant numbers is a 3-brilliant number. 37789 = 23 * 31 * 53 = 4 + 6 + 9 + 10 + 14 + 15 + 21 + 25 + 35 + 49 + 121 + 143 + 169 + 187 + 209 + 221 + 247 + 253 + 289 + 299 + 319 + 323 + 341 + 361 + 377 + 391 + 403 + 407 + 437 + 451 + 473 + 481 + 493 + 517 + 527 + 529 + 533 + 551 + 559 + 583 + 589 + 611 + 629 + 649 + 667 + 671 + 689 + 697 + 703 + 713 + 731 + 737 + 767 + 779 + 781 + 793 + 799 + 803 + 817 + 841 + 851 + 869 + 871 + 893 + 899 + 901 + 913 + 923 + 943 + 949 + 961 + 979 + 989 - Jonathan Vos Post, Jun 17 2007
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(5) = 10013 = 17 * 19 * 31 and there is no lesser number of five digits which has three prime factors, not necessarily different, of the same size in decimal notation.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
