A083128 Least 3-brilliant number of size n.

8, 12, 105, 1331, 10013, 100181, 1030301, 10000127, 100000727, 1027243729, 10000002797, 100000000757, 1002101470343, 10000000000493, 100000000005643, 1000090002700027, 10000000000001251, 100000000000000649

Offset: 1

Author

Robert G. Wilson v, May 11 2003

Keywords

• nonn
• base

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

Examples

			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.
		

Links

• Dario Alpern, Brilliant numbers

Crossrefs

Cf. A083182.

Cf. A078972, A083128, A083182.