43 (number)

 ← 42 43 44 →
Cardinal forty-three
Ordinal 43rd
(forty-third)
Factorization prime
Divisors 1, 43
Roman numeral XLIII
Binary 1010112
Ternary 11213
Quaternary 2234
Quinary 1335
Senary 1116
Octal 538
Duodecimal 3712
Vigesimal 2320
Base 36 1736

43 (forty-three) is the natural number following 42 and preceding 44.

In mathematics

Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime.[1]

43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 × 3 × 7).[2]

43 is a centered heptagonal number.[3]

Let a0 = a1 = 1, and thenceforth an = 1/n − 1(a02 + a12 + ... + an − 12). This sequence continues 1, 1, 2, 3, 5, 10, 28, 154... (sequence A003504 in the OEIS). a43 is the first term of this sequence that is not an integer.

43 is a Heegner number.[4]

43 is a repdigit in base 6 (111).

43 is the largest natural number that is not a (original) McNugget number.[5]

 4 15 17 7 5 19 13 6 20 9 2 12 14 0 11 18

This is the smallest prime number expressible as the sum of 2, 3, 4, or 5 different primes:

• 43 = 41 + 2
• 43 = 11 + 13 + 19
• 43 = 2 + 11 + 13 + 17
• 43 = 3 + 5 + 7 + 11 + 17.

The date magic square at right illustrates the magic constant as the sum of four primes:

When taking the first six terms of the Taylor series for computing e, one obtains

${\displaystyle \sum _{i=0}^{5}{\frac {1}{i!}}={\frac {163}{60}}=2+{\frac {43}{60}},\ }$

which is also five minus the fifth harmonic number.

Every solvable configuration of the Fifteen puzzle can be solved in no more than 43 multi-tile moves (i.e. when moving two or three tiles at once is counted as one move).[6]

In sports

In the US's National Football League, the number 43 was worn by Jim Norton of the Houston Oilers. The Oilers (now the Tennessee Titans) retired the number.

In auto racing:

• Brad Daugherty, ESPN NASCAR analyst and retired American basketball player. His #43 jersey, a number he picked as a tribute to NASCAR legend Richard Petty (whom Daugherty lists as his favorite sportsman), was retired by the Cavaliers on March 1, 1997.

In baseball:

In Motocross/Supercross

• Joey Savatgy ran the number 43 in the 2014 250MX and 250SX series and was sponsored by Armswag.

Arts, entertainment, and media

Popular culture

• Movie 43 (2013) is a film consisting of a series of interconnected short stories, featuring some of the biggest stars in Hollywood, which make up the insane storylines a washed-up producer is pitching to a movie company.
• In The Big Bang Theory episode "The 43 Peculiarity", Howard and Raj try to solve the mystery of Sheldon disappearing every afternoon to a room with a chalkboard that has the number 43 written on it.
• Odd Squad Agent 43 is one of the main villains: Agent Todd who later was fired for causing oddness. Odd Todd now gave up doing odd and now works in a community garden.

Forty-three is:

Notes

1. ^ "Sloane's A000979 : Wagstaff primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ "Sloane's A065003 : Not McNugget numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
6. ^ "The Fifteen Puzzle can be solved in 43 "moves"". Domain of the Cube Forum
7. ^ Kellogg, William O. (2010). Barron's AP United States History (9th ed.). Barron's Educational Series. p. 364. ISBN 9780764141843. George H. W. Bush (Republican) [Bush 41—i.e., the first president Bush, George H. W. Bush was the forty-first President of the United States, and so some have referred to him in this way since the election of his son, George W. Bush or Bush 43—the forty-third president of the United States.]