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

1,1

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

Table of n, a(n) for n=1..18.

Dario Alpern, Brilliant numbers

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

Cf. A083182.

Cf. A078972, A083128, A083182.

Sequence in context: A266800 A230545 A180922 * A196077 A067923 A258780

Adjacent sequences: A083125 A083126 A083127 * A083129 A083130 A083131

Keyword

nonn,base

Author

Robert G. Wilson v, May 11 2003

Status

approved