41

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41 is a prime number.

Membership in core sequences

Odd numbers	..., 35, 37, 39, 41, 43, 45, 47, ...	A005408
Prime numbers	..., 29, 31, 37, 41, 43, 47, 53, ...	A000040
Squarefree numbers	..., 37, 38, 39, 41, 42, 43, 46, ...	A005117
Numerators of continued fraction convergents to $\sqrt{2}$	1, 1, 3, 7, 17, 41, 99, 239, 577, ...	A001333

In Pascal's triangle, 41 occurs twice.

Sequences pertaining to 41

Multiples of 41	0, 41, 82, 123, 164, 205, 246, 287, 328, 369, 410, 451, 492, ...
$3x+1$ sequence beginning at 27	27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, ...	A008884

Partitions of 41

There are 44583 partitions of 41. Of these, [FINISH WRITING]

Roots and powers of 41

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

$\sqrt{41}$	6.40312423	A010495	41 2	1681
$\sqrt[3]{41}$	3.44821724	A010612	41 3	68921
$\sqrt[4]{41}$	2.53043953	A011035	41 4	2825761
$\sqrt[5]{41}$	2.10163247	A011126	41 5	115856201
$\sqrt[6]{41}$	1.85693759		41 6	4750104241
$\sqrt[7]{41}$	1.69979948		41 7	194754273881
$\sqrt[8]{41}$	1.59073553		41 8	7984925229121
$\sqrt[9]{41}$	1.51076949		41 9	327381934393961
$\sqrt[10]{41}$	1.44970082		41 10	13422659310152401
				A009985

Logarithms and 41st powers

REMARKS

TABLE

Values for number theoretic functions with 41 as an argument

TABLE GOES HERE

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −41, 41

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Factorization of 41 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

Representation of 41 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	101001	1112	221	131	105	56	51	45	41	38	35	32	2D	2B	29	27	25	23	21

See also

Some integers

							$-1$
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