A147764 Elias omega coded prime numbers represented in decimal.

8, 12, 84, 92, 236, 244, 2628, 2636, 2652, 2676, 2684, 5524, 5540, 5548, 5564, 5588, 5612, 5620, 11532, 11548, 11556, 11580, 11596, 11620, 11652, 11668, 11676, 11692, 11700, 11716, 11772, 24076, 24100, 24108, 24148, 24156, 24180, 24204, 24220

Offset: 1

Author

Reikku Kulon, Nov 11 2008

Keywords

• base
• easy
• nonn

Comments

The sequence in binary begins:

2 1000

3 1100

5 1010100

7 1011100

The final 0 bit represents an exponent of 1.

Because this is a prefix code, there is a one-to-one mapping between the integers and integers representing their factors, provided that the coded factors and exponents are adequately delimited, such as by inserting additional 0 bits.

For example, 75600 = 2^4 * 3^3 * 5^2 * 7 is representable as 100^101000 110^110 101010^100 101110^0 -> 1001010000110110010101010001011100 = 9946354780 decimal.

This representation is unambiguous because, e.g., the incorrect reading 1001010000110 splits as 100101000 0110 or 100^101000 0^110 -> 2^4 * 1^3, which is clearly wrong.