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29

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Please do not rely on any information it contains.            


29 is an integer.

Membership in core sequences

Odd numbers ..., 23, 25, 27, 29, 31, 33, 35, ... A005408
Prime numbers ..., 17, 19, 23, 29, 31, 37, 41, ... A000040
Squarefree numbers ..., 22, 23, 26, 29, 30, 31, 33, ... A005117
Lucas numbers ..., 7, 11, 18, 29, 47, 76, 123, ... A000032
Pell numbers ..., 2, 5, 12, 29, 70, 169, 408, ... A000129
Central polygonal numbers ..., 11, 16, 22, 29, 37, 46, 56, ... A000124

In Pascal's triangle, 29 occurs twice. (In Lozanić's triangle, 29 occurs four times).

Sequences pertaining to 29

Multiples of 29 0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, ... A195819
29-gonal numbers 1, 29, 84, 166, 275, 411, 574, 764, 981, 1225, 1496, 1794, ... A255187
29-gonal pyramidal numbers 1, 30, 114, 280, 555, 966, 1540, 2304, 3285, 4510, 6006, ... A256649
Primes with primitive root 29 2, 3, 11, 17, 19, 41, 43, 47, 73, 79, 89, 97, 101, 113, 127, ... A019355
sequence starting at 51 51, 154, 77, 232, 116, 58, 29, 88, 44, 22, 11, 34, 17, 52, ... A033479
sequence starting at 7 7, 36, 18, 9, 46, 23, 116, 58, 29, 146, 73, 366, 183, 916, ... A028389

Partitions of 29

There are 4565 partitions of 29.

The Goldbach representations of 29 using distinct primes are: 3 + 7 + 19 = 5 + 7 + 17 = 5 + 11 + 13 = 29.

Roots and powers of 29

In the table below, irrational numbers are given truncated to eight decimal places.

5.38516480 A010484 29 2 841
3.07231682 A010600 29 3 24389
2.32059578 A011024 29 4 707281
1.96100905 A011114 29 5 20511149
1.75280256 29 6 594823321
1.61775965 29 7 17249876309
1.52335018 29 8 500246412961
1.45374644 29 9 14507145975869
1.40036033 29 10 420707233300201
A009973

Logarithms and 29th powers

In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.

If is not a multiple of 59, then either or is. Hence the formula for the Legendre symbol .

As above, irrational numbers in the following table are truncated to eight decimal places.

0.20584683 4.85798099 2 29 536870912
0.29697420 3.36729582 A016652 3931334297144.04207438
0.32625951 3.06504475 3 29 68630377364883
0.41169366 2.42899049 4 29 288230376151711744
0.47796154 2.09221853 5 29 186264514923095703125
0.53210634 1.87932358 6 29 36845653286788892983296
0.57788511 1.73044774 7 29 3219905755813179726837607
0.61754049 1.61932699 8 29 154742504910672534362390528
0.65251902 1.53252237 9 29 4710128697246244834921603689
0.68380837 1.46239799 10 29 100000000000000000000000000000

See A122970 for the 29th powers of integers.

Values for number theoretic functions with 29 as an argument

−1
−2
10
30
2
28
1
1
28 This is the Carmichael lambda function.
−1 This is the Liouville lambda function.
29! 8841761993739701954543616000000
304888344611713860501504000000

Factorization of some small integers in a quadratic integer ring adjoining square roots of −29, 29

is a unique factorization domain, is not. Units in are of the form . Units in are just 1 and −1.

2 Irreducible Prime
3
4 2 2
5 Irreducible
6 2 × 3
7 Prime
8 2 3
9 3 2
10 2 × 5
11 Irreducible Prime
12 2 2 × 3
13 Irreducible
14 2 × 7
15 3 × 5
16 2 4
17 Prime
18 2 × 3 2
19 Irreducible Prime
20 2 2 × 5
21 3 × 7
22 2 × 11
23 Prime
24 2 3 × 3
25 5 2
26 2 × 13
27 3 3
28 2 2 × 7
29
30 2 × 3 × 5 OR
31 Prime
32 2 5
33 3 × 11 OR 3 × 11
34 2 × 17
35 5 × 7
36 2 2 × 3 2
37
38 2 × 19 OR 2 × 19
39 3 × 13
40 2 3 × 5

has class number 6. Here we will exhibit a few more examples of numbers with more than one distinct factorization in in which the factorizations have differing numbers of irreducible factors.

45 3 2 × 5 OR
54 2 × 3 3 OR
78 2 × 3 × 13 OR
110 2 × 5 × 11 OR
117 3 2 × 13 OR
120 2 3 × 3 × 5 OR
125 5 3 OR

Ideals really help us make sense of multiple distinct factorizations in , while raising some questions about .

Factorization of
In In
2 Prime
3
5
7 Prime
11 Prime
13
17 Prime
19 Prime
23 Prime
29
31
37
41
43
47

Factorization of 29 in some quadratic integer rings

As was mentioned above, 29 is a prime number in . But it is composite in some quadratic integer rings.

Prime Prime
Irreducible
Prime
Irreducible Irreducible
Prime Prime
Irreducible
Prime
Prime

Representation of 29 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 11101 1002 131 104 45 41 35 32 29 27 25 23 21 1E 1D 1C 1B 1A 19

See also

Some integers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
1729