A108880 Alphabetically earliest number that is a product of exactly n primes.

8018018851, 8000000018, 8, 8018000018, 8018018886, 8018018085, 8018018808, 8000000008, 8018018000, 8018018048, 8018018816, 8018018176, 8018808000, 8018808832, 8018000000, 8018018304, 8018887680, 8018804736, 8018853888

Offset

1,1

Comments

Conway and Guy note that 8018018851 is, alphabetically, the first prime number in the American system of large number terminology and term this "Knuth's number." We have "eight billion" alphabetically before "eighteen" or "eighty."

References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 15, 1996.

Links

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Almost Prime.

Example

n Alphabetically first n-almost prime
1 8018018851
2 8000000018 = 2 * 4000000009
3 8 = 2^3
4 8018000018 = 2 * 7 * 97 * 5904271
5 8018018886 = 2 * 3 * 19 * 6661 * 10559
6 8018018085 = 3 * 5 * 7 * 11 * 163 * 42589
7 8018018808 = 2^3 * 3 * 31 * 2161 * 4987
8 8000000008 = 2^3 * 7 * 11 * 13 * 19 * 52579
9 8018018000 = 2^4 * 5^3 * 127 * 31567
10 8018018048 = 2^8 * 43 * 728381

Crossrefs

Cf. A000052.

Sequence in context: A364436 A075131 A250865 * A204500 A290539 A017003

Adjacent sequences: A108877 A108878 A108879 * A108881 A108882 A108883

Keyword

nonn,word

Author

Jonathan Vos Post, Jul 14 2005

Extensions

Corrected and extended by Ray Chandler, Jul 25 2005

Definition clarified by N. J. A. Sloane, Sep 27 2011

Status

approved