## Leonhard Euler was born on this day 309 years ago.

### Properties of the number 4229:

4229 and 4231 form a twin prime pair.4229 has 5 antidivisors and 4228 totatives.

4229 has an emirp digit sum 17 in base 10.

4229 has a Fibonacci digit product 144 in base 10.

4229 = 2115

^{2}- 2114

^{2}is the difference of 2 nonnegative squares in 1 way.

4229 is the difference of 2 positive pentagonal numbers in 1 way.

4229 = 2

^{2}+ 65

^{2}is the sum of 2 positive squares in 1 way.

4229 = 2

^{2}+ 33

^{2}+ 56

^{2}is the sum of 3 positive squares.

4229

^{2}= 260

^{2}+ 4221

^{2}is the sum of 2 positive squares in 1 way.

4229

^{2}is the sum of 3 positive squares.

4229 is a divisor of 1213

^{28}- 1.

4229 = '422' + '9' is the concatenation of 2 semiprime numbers.

4229 is an emirp in (at least) the following bases: 2, 7, 9, 11, 18, 23, 24, 28, 37, 41, 45, 46, 48, 50, 51, 55, 56, 57, 65, 67, 73, 76, 77, 79, 81, 83, 92, and 97.

4229 is palindromic in (at least) base 19.

4229 in base 19 = bdb and consists of only the digits 'b' and 'd'.

4229 in base 26 = 66h and consists of only the digits '6' and 'h'.

4229 in base 32 = 445 and consists of only the digits '4' and '5'.

4229 in base 37 = 33B and consists of only the digits '3' and 'B'.

### The number 4229 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A005473: Primes of form n^2 + 4.

A015523: a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=0, a(1)=1.

A078370: 4*(n+1)*n + 5.

A084740: Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists.

A089392: Magnanimous primes: primes with the property that inserting a "+" in any place between two digits yields a sum which is prime.

A113228: a(n) is the number of permutations of [1..n] that avoid the consecutive pattern 1324 (equally, the number that avoid 4231).

A174913: Lesser of twin primes p1 such that 2*p1+p2 is a prime number.

A175965: Lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.

A192476: Monotonic ordering of set S generated by these rules: if x and y are in S then x^2 + y^2 is in S, and 1 is in S.

A264173: Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive pattern 1324; triangle T(n,k), n>=0, 0<=k<=max(0,floor(n/2-1)), read by rows.

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