Properties
W.L. McDaniel in 1987 proved that there are infinitely many Smith numbers. The number of Smith numbers below 10n for n=1,2,… is:
- 1, 6, 49, 376, 3294, 29928, 278411, 2632758, 25154060, 241882509, … (sequence A104170 in OEIS)
Two consecutive Smith numbers (for example, 728 and 729, or 2964 and 2965) are called Smith brothers. It is not known how many Smith brothers there are. The starting elements of the smallest Smith n-tuple for n=1,2,… are:
- 4, 728, 73615, 4463535, 15966114, 2050918644, 164736913905, … (sequence A059754 in OEIS)
Smith numbers can be constructed from factored repunits. The largest known Smith number as of 2010 is:
- 9 × R1031 × (104594 + 3×102,297 + 1)1476 ×103,913,210
where R1031 is a repunit equal to (101031−1)/9.
Read more about this topic: Smith Number
Famous quotes containing the word properties:
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—John Locke (1632–1704)
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