Numbers
What follows is the collaborative collection of numbers and interesting things about them from 1 to 365. Some are more interesting than others, there are some gaps, but most of what is listed below is a collection from various sources and people. Some of what is listed was “discovered” by me, but it was mostly just collected and “curated” by me. The list is aimed at all audiences, intended to be as simple as possible, and only for amusement and teaching/education. References and/or resources are listed.
The following people, in no particular order, have somehow contributed to or inspired this list: Pat Ballew, Gary Davis, David Coffey, Earl Samuelson, Ben Vitale, Alex Bogomolny, Colin Wright, Dan Hagon, Colm Mulcahy, Owen O’Shea, Caroline Wilder, Sue Wood, Scott Cram, Derek Orr, Vincent Pantaloni, Patrick Honner, Simon Pampena, Dave Radcliffe, and Dave Richeson. If you find an error, find an oversight, or would like to fill a gap, please contact me.
To start, find out what day of the year it is here!
And now for a few numbers from 1 – 121:
1: 1 is the first counting number, but not the first number listed in the dictionary… what is?
2: An honest number (the same number of letters as its value) in Danish- to
3: An honest number (the same number of letters as its value) in Danish- tre
4: A black hole number in English… count the letters in any number, write out the name of the number you counted, repeat the process, you will not escape four!
5: An honest number in Spanish- cinco
6: A perfect number and also 6 = 1+2+3 and 1•2•3
7: 74 = 2401 = (2+4+0+1)4
8: 83 = 512 = (5+1+2) 3
9: 9 = 1!+2!+3! and can be written upside down in base 2 as 1001.
10: 10 = 1+2+3+4
11: The only palindromic prime with an even number of digits
12: 122 = 144 and 212 = 441
13: 132 = 169 and 312 = 961
14: A Keith Number: 1+4=5, 4+5=9, and 9+5=14
15: 1+2+3+4+5
17: 173 = (4+9+1+3)3 = 4913
18: 183 = (5+8+3+2)3 = 5832
19: A Keith Number: 1+9=10 and 9+10=19
20: The number of vertices of a dodecahedron
21: 212 = 441 and 122 = 144
22: 14 + 23 + 32 + 41
23: 23! has 23 digits!
24: 24! has 24 digits!
26: 263 = 17576 and 1+7+5+7+6 = 26
27: 273 = (1+9+6+8+3)3
28: A Perfect Number and a Keith Number- 28: 2+8=10, 8+10=18, and 10+18=28
29: As an honest number, 29 = the largest prime less than thirty
30: Number of Post-it Notes required for a dodecahedron
31: As noted earlier, 31 is the reverse of 13. The same is true of their squares- 961 & 169. Also, 31+32= 33 + 13 + 33 + 23
32: 11 + 22 + 33
33: 1!+2!+3!+4!
34: 33 + 23 – 1 3 = 34
36: A Wilder Number? 362 = 1296 and 1 + 29 + 6 = 36
37: 33 + 73 = 37 • (3+7)
39: 39 + 343 = 39343
40: The only number in English with the letters in ABC order
43: 43 • 68 = 86 • 34
44: !5 = 44
45: A Kaprekar Number 452 = 2025 and 20+25=45
47: A Keith Number: 4+7=11, 7+11=18, 11+18=29, and 18+29=47
48: 48 • (4+8) = 43 + 83
49: √49 = -√4 + 9
51: The smallest number that can be made with numbers 1 to 5 using only primes
52: A Reverse Keith Number: 5+2=7, 2+7=9, 7+9=16, and 9+16=25
55: 552 = 3025 and 30+25=55
64: √64 = 6 + √4
65: 15 + 24 + 33 + 42 + 51
69: ¡uʍop ǝpısdn ǝɯɐs ǝɥʇ spɐǝɹ 69
71: 712 = 7!+1!
72: 72 = 24 • 3 and 24 + 3 = 27
75: A Keith Number 7+5=12, 5+12=17, 12+17=29, 17+29=46, 29+46=75
77: The smallest number in English that requires 5 syllables for its expression… did you check?
81: 33 + 33 + 33
83: 832 = 6889 which reads the same upside down!
88: 88|33 and 882 + 332 = 8833
90: The number of degress in a right angle
94: 94 = 47 • 2 and 47 + 2 = 49
99: 992 = 9801 and 98 + 01 = 99
100: 1+2+3+4+5+6+7+ (8•9)
101: 102 + 12
102: 102 is the reverse of 201. The same is true of their squares: 1022 = 10404 and 2012 = 40401.
103: 103 is the reverse of 301. The same is true of their squares: 1032 = 10609 and 3012 = 90601.
111: 371 + 371 + 371
112: 112 is the reverse of 211. The same is true of their squares: 1122 = 12544 and 2112 = 44521.
120: 5!
121: √121 = 12-1
References:
Ecker, M. Number play, calculators, and card tricks: Mathemagical black holes. Retrieved from http://g4gardner.pbworks.com/f/mm-ecker.pdf
Gardner, M. (1986). Knotted doughnuts and other mathematical entertainments. New York: W.H. Freeman and Company.
Gardner, M. (1976). The incredible dr. matrix. New York: Charles Scribner’s Sons.
Kordemsky, B. (1972). The moscow puzzles: 359 mathematical recreations. New York: Dover Publications, Inc.
O’Shea, O. & Dudley, U. (2007). The magic numbers of the professor. Washington, DC: The Mathematical Association of America, Inc.
Posamentier, A. & Leimann, I. (2009). Mathematical amazements and surprises: Fascinating figures and noteworthy numbers. New York: Prometheus Books.
Prime Curios! (2000). https://primes.utm.edu/curios/
Sallows, L. (1986). Alphamagic squares. Abacus, 4, 28-45.
Weisstein, Eric W. “Vampire Number.” From MathWorld–A Wolfram Web Resource http://mathworld.wolfram.com/VampireNumber.html Accessed 7 October 2012
Wells, D. (1997). The penguin dictionary of curious and interesting numbers. New York: Penguin Putnam Inc.
Jim,
I’m loving this. Guess where I will be stealing stuff each day. Keep up the good work.
113 has the same square relation with 311 as 112 and 211 as you already knew but haven’t yet added.
for 114 I have that the first 114 digits of e (after the decimal point) form a prime but that is not the numeric kind of thing most of these are…
FOr 116, I have 116!+1 is prime.
Pat B
For 105 The 105th day of the year, Paul Erdős conjectured that this is the largest number n such that the positive values of n – 2k are all prime.