From Wikipedia, the free encyclopedia
Natural number
181 (one hundred [and] eighty-one ) is the
natural number following
180 and preceding
182 .
In mathematics
181 is
prime , and a
palindromic ,
[1]
strobogrammatic ,
[2] and
dihedral number
[3] in
decimal . 181 is a
Chen prime .
[4]
181 is a
twin prime with
179 ,
[5] equal to the sum of five consecutive prime numbers:
[6]
29 +
31 +
37 +
41 +
43 .
181 is the difference of
two consecutive
square numbers 912 – 902 ,
[7] as well as the sum of two consecutive squares: 92 + 102 .
[8]
As a
centered polygonal number ,
[9] 181 is:
181 is also a centered (
hexagram )
star number ,
[11] as in the game of
Chinese checkers .
Specifically, 181 is the 42 nd prime number
[13] and 16th
full reptend prime in
decimal ,
[14] where multiples of its
reciprocal
1
181
{\displaystyle {\tfrac {1}{181}}}
inside a
prime reciprocal magic square repeat
180 digits with a
magic sum
M
{\displaystyle M}
of
810 ; this value is one less than
811 , the 141 st prime number and 49th full reptend prime (or equivalently long prime ) in decimal whose reciprocal
repeats 810 digits. While the first full non-normal prime reciprocal magic square is based on
1
19
{\displaystyle {\tfrac {1}{19}}}
with a magic constant of
81 from a
18
×
18
{\displaystyle 18\times 18}
square,
[15] a normal
19
×
19
{\displaystyle 19\times 19}
magic square has a magic constant
M
19
=
19
×
181
{\displaystyle M_{19}=19\times 181}
;
[16] the next such full, prime reciprocal magic square is based on multiples of the reciprocal of
383 (also palindromic ).
[17]
[a]
181 is an
undulating number in
ternary and
nonary
numeral systems , while in
decimal it is the 28th
undulating prime .
[18]
In other fields
181 is also:
See also
References
^ Where the full reptend index of 181 is 16 = 42 , the such index of 811 is 49 = 72 . Note, also, that
282 is 141 × 2.
^
Sloane, N. J. A. (ed.).
"Sequence A002385 (Palindromic primes: prime numbers whose decimal expansion is a palindrome.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A007597 (Strobogrammatic primes.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A134996 (Dihedral calculator primes: p, p upside down, p in a mirror, p upside-down-and-in-a-mirror are all primes.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26 .
^
Sloane, N. J. A. (ed.).
"Sequence A006512 (Greater of twin primes.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A034964 (Sums of five consecutive primes.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A024352 (Numbers which are the difference of two positive squares, c^2 - b^2 with 1 less than or equal to b less than c.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A001844 (Centered square numbers: a(n) equal to 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z is Y+1) ordered by increasing Z; then sequence gives Z values.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26 .
^
a
b
Sloane, N. J. A. (ed.).
"Centered polygonal numbers" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A005891 (Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A003154 (Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26 .
^
Sloane, N. J. A. (ed.).
"Sequence A069131 (Centered 18-gonal numbers.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26 .
^
Sloane, N. J. A. (ed.).
"Sequence A000040 (The prime numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A001913 (Full reptend primes: primes with primitive root 10.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^ Andrews, William Symes (1917).
Magic Squares and Cubes (PDF) . Chicago, IL:
Open Court Publishing Company . pp. 176, 177.
ISBN
9780486206585 .
MR
0114763 .
OCLC
1136401 .
Zbl
1003.05500 .
^
Sloane, N. J. A. (ed.).
"Sequence A006003 (a(n) equal to n*(n^2 + 1)/2.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
Sloane, N. J. A. (ed.).
"Sequence A072359 (Primes p such that the p-1 digits of the decimal expansion of k/p (for k equal to 1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-09-04 .
^
Sloane, N. J. A. (ed.).
"Sequence A032758 (Undulating primes (digits alternate).)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
External links
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