Affluent Savvy
Photo by Harry Cooke Pexels Logo Photo: Harry Cooke

Is 666 a Smith number?

Mathematical definition The first few Smith numbers in base 10 are: 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086 …

en.wikipedia.org - Smith number - Wikipedia
What should you not forget in your luggage?
What should you not forget in your luggage?

Most Commonly Forgotten Things to Pack Don't Forget Travel Documents. ... One of the Most Commonly Forgotten Things to Pack Are Snacks. ... Keep a...

Read More »
Last updated Aug 18, 2020
How to make money with no money?
How to make money with no money?

Summary: How to make money for free in 2022 Become a virtual assistant. Do research online. Transcribe audio and video files. Set up a Patreon....

Read More »
Last updated Jan 25, 2022
Awaken your dormant DNA ability to attract wealth effortlessly
Awaken your dormant DNA ability to attract wealth effortlessly

The simple yet scientifically proven Wealth DNA method laid out in the report allows you to effortlessly start attracting the wealth and abundance you deserve.

Learn More »
Promotion

Type of composite integer

In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed. Smith numbers were named by Albert Wilansky of Lehigh University, as he noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:

4937775 = 31 52 658371

while

4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 · 1 + 5 · 2 + (6 + 5 + 8 + 3 + 7) · 1 = 42

in base 10.[1]

Mathematical definition [ edit ]

Let n {\displaystyle n} be a natural number. For base b > 1 {\displaystyle b>1} , let the function F b ( n ) {\displaystyle F_{b}(n)} be the digit sum of n in base b {\displaystyle b} . A natural number n {\displaystyle n} has the integer factorisation n = ∏ p prime p ∣ n p v p ( n ) {\displaystyle n=\prod _{\stackrel {p\mid n}{p{\text{ prime}}}}p^{v_{p}(n)}}

and is a Smith number if

F b ( n ) = ∑ p prime p ∣ n v p ( n ) F b ( p ) {\displaystyle F_{b}(n)=\sum _{\stackrel {p\mid n}{p{\text{ prime}}}}v_{p}(n)F_{b}(p)} where v p ( n ) {\displaystyle v_{p}(n)} is the p-adic valuation of n {\displaystyle n} . For example, in base 10, 378 = 21 33 71 is a Smith number since 3 + 7 + 8 = 2 · 1 + 3 · 3 + 7 · 1, and 22 = 21 111 is a Smith number, because 2 + 2 = 2 · 1 + (1 + 1) · 1

The first few Smith numbers in base 10 are:

4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086 … (sequence A006753 OEIS)

Properties [ edit ]

W.L. McDaniel in 1987 proved that there are infinitely many Smith numbers.[1][2] The number of Smith numbers in base 10 below 10n for n=1,2,... is: Two consecutive Smith numbers (for example, 728 and 729, or 2964 and 2965) are called Smith brothers.[3] It is not known how many Smith brothers there are. The starting elements of the smallest Smith n-tuple (meaning n consecutive Smith numbers) in base 10 for n = 1, 2, ... are:[4] Smith numbers can be constructed from factored repunits. The largest known Smith number in base 10 as of 2010 is: 9 × R 1031 × (104594 + 3 × 10 2297 + 1)1476 × 10 3 913 210

where R 1031 is a repunit equal to (101031−1)/9.

See also [ edit ]

Notes [ edit ]

What bird is the Holy Spirit?
What bird is the Holy Spirit?

Dove The Holy Spirit as a Dove Perhaps the most powerful avian symbol is the dove representing the Holy Spirit, which can be found throughout the...

Read More »
Last updated Oct 5, 2019
What can I put outside my front door for luck?
What can I put outside my front door for luck?

A horseshoe is one of the most common decorations for attracting good luck to your home. Traditionally, the horseshoe should be hung above the...

Read More »
Last updated May 14, 2018
Awaken your dormant DNA ability to attract wealth effortlessly
Awaken your dormant DNA ability to attract wealth effortlessly

The simple yet scientifically proven Wealth DNA method laid out in the report allows you to effortlessly start attracting the wealth and abundance you deserve.

Learn More »
Promotion

What is the platinum rule?
What is the platinum rule?

Most of us grew up with the Golden Rule (Do unto others as you would have them do unto you). The “Platinum Rule” is a common business buzzword. The...

Read More »
Last updated Mar 16, 2020
What jobs can I make 70k without a degree?
What jobs can I make 70k without a degree?

Best Jobs That Don't Require a Degree and Pay $70K a Year: At a Glance Job Average Salary Top 10% Dental Hygienists $77,090 $104,420+ Agricultural...

Read More »
Last updated May 30, 2019
Awaken your dormant DNA ability to attract wealth effortlessly
Awaken your dormant DNA ability to attract wealth effortlessly

The simple yet scientifically proven Wealth DNA method laid out in the report allows you to effortlessly start attracting the wealth and abundance you deserve.

Learn More »
Promotion
How long would it take to save $50,000?
How long would it take to save $50,000?

Compare that to each person saving 15% of their take-home pay, the savings rate typically recommended by experts. In that case, it would take six...

Read More »
Last updated Mar 24, 2021
Awaken your dormant DNA ability to attract wealth effortlessly
Awaken your dormant DNA ability to attract wealth effortlessly

The simple yet scientifically proven Wealth DNA method laid out in the report allows you to effortlessly start attracting the wealth and abundance you deserve.

Learn More »
Promotion
Is having 2 zodiac signs possible?
Is having 2 zodiac signs possible?

No matter your birth date, there's only one answer -- no one actually has two signs. But if you were born within a few days of the Sun's move from...

Read More »
Last updated Apr 28, 2020