Next month will be the 124th Carnival of Mathematics, so let's prepare a little for the occasion.
124 = 2 * 2 * 31 (this is its prime
factorization).
It has 6 divisors (1, 2, 4, 31, 62, 124),
whose sum is σ = 224. Its totient is φ = 60.
The sum of its prime factors is 35 (or 33 counting only the distinct
ones). The product of its digits is 8,
while the sum is 7.
124 is an amenable, composite, congruent,
deficient, even, iccanobiF, nude, pernicious, polite, odious, untouchable and
wasteful number.
124 is nontrivially palindromic and
repdigit when written in base 5: 4445.
It is one of the 548 Lynch-Bell numbers.
It is a plaindrome in base 5, base 7, base
9, base 10, base 14 and base 16. It is a
nialpdrome in base 2, base 5, base 12, base 13 and base 15. It is a zygodrome in base 2 and base 5.
24 is the hypotenuse of at least one
Pythagorean triangle.
124 is a 3-almost prime.
124 is a Loeschian number.
124 is the nearest integer to imaginary
part of 41st zero of Riemann zeta function.
124 can be expressed as the sum of 4 (but
no fewer) non-zero squares.
There 2,841,940,500 partitions of 124.
124 straight slices can cut a cake into
317,875 pieces (the 124th Cake number).
124 straight cuts can divide a pizza or
pancake into 7751 pieces (the 124th Lazy Caterer number).
Mordell's equation (y^2 = x^3 + n) has no
integral solutions when n = 124.
124 is a Stella Octangula number.
124 is divisible by every digit in 124.
There are 124 benzenoids with 23 hexagons,
C_(2v) symmetry and containing 69 carbon atoms.
124 cannot be expressed as the hypotenuse
of a Pythagorean triple.
There are 124 squares and rectangles after
20 stages in the toothpick structure.
This structure contains 207 toothpicks.
At stage 124, the structure will contain 8971 toothpicks.
124 is a Belgian-2 number, a Belgian-4
number, a Belgian-5 number, and a Belgian-9 number.
124 is the sum of eight consecutive primes:
124 = 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.
124 = 27 - 22.
124 = 52 + 52 + 52 + 72.
The string 124 occurs at position 1080,
counting from the first digit after the decimal point (the “3.” is not
counted). This string occurs 199,797
times in the first 200 million digits of Pi.
124 is a palindromic and repdigit number
when written in base 30: 4430.
124 is the smallest number whose sum of
digits as well as the number itself are one less than the cube of a prime.
[Gupta]
The sum of the 3rd to 10th prime numbers (5
+ 7 + ... + 29 = 124). [Thoms]
124 = sigma(1! * 2! * 4!). Note that 124 is
the smallest multi-digit number with this property. [Firoozbakht]
124 can be expressed as the difference of
two squares: 124 = 322 - 302.
124 can be expressed as the sum of two
prime numbers in 5 different ways: 124 = 113 + 11 = 107 + 17 = 101 + 23 = 83 +
41 = 71 + 53.
124 written as a Greek numeral is ρκδʹ.
124 written as a Chinese numeral is 一百二十四.
124 written as a Hebrew numeral is קכד.
124 written as an Arabic numeral is ١٢٤.
124 written as a Roman numeral is CXXIV.
124 written as a Maya numeral is:
●
▃▃▃▃▃
●●●●
124 is a 22-gonal number.
124 is the short leg of at least one
Pythagorean triple: 1242 + 19202 =
19242.
The 124th pair of Amicable numbers are
13,813,150, and 14,310,050.
The 124th set of Sociable numbers are
100,805,144,361,379,855,289,068, 103,831,608,305,414,552,892,692,
106,948,916,760,522,865,797,868, and 103,831,603,731,649,764,832,532.
|
The decimal expansion of the inverse of 806,451,612,903,224,193,548,387,096,775
produces a digital sequence that shows the multiples of 124, written in 15
digit strings (each term is separated by spaces to make reading easier).
1/806451612903224193548387096775 =
0.
000000000000000 000000000000124 000000000000248 000000000000372 000000000000496 000000000000620 000000000000744 000000000000868 000000000000992 000000000001116 000000000001240 000000000001364 000000000001488 000000000001612 000000000001736 000000000001860 000000000001984 000000000002108 000000000002232 000000000002356 000000000002480 000000000002604 000000000002728 000000000002852 000000000002976 000000000003100 000000000003224 000000000003348 000000000003472 000000000003596 000000000003720 000000000003844 000000000003968 000000000004092 000000000004216 000000000004340 000000000004464 000000000004588 000000000004712 000000000004836 000000000004960 000000000005084 000000000005208 000000000005332 000000000005456 000000000005580 000000000005704 000000000005828 000000000005952 000000000006076 000000000006200 000000000006324 000000000006448 000000000006572 000000000006696 000000000006820 000000000006944 000000000007068 000000000007192 000000000007316 000000000007440 000000000007564 000000000007688 000000000007812 000000000007936 000000000008060 000000000008184 000000000008308 000000000008432 000000000008556 000000000008680 000000000008804 000000000008928 000000000009052 000000000009176 000000000009300 000000000009424 000000000009548 000000000009672 000000000009796 000000000009920 000000000010044 000000000010168 000000000010292 000000000010416 000000000010540 000000000010664 000000000010788 000000000010912 000000000011036 000000000011160 000000000011284 000000000011408 000000000011532 000000000011656 000000000011780 000000000011904 000000000012028 000000000012152 000000000012276 000000000012400 000000000012524 000000000012648 000000000012772 000000000012896 000000000013020 000000000013144 000000000013268 000000000013392 000000000013516 000000000013640 000000000013764 000000000013888 000000000014012 000000000014136 000000000014260 000000000014384 000000000014508 000000000014632 000000000014756 000000000014880 000000000015004 000000000015128 000000000015252 000000000015376 000000000015500 000000000015624 000000000015748 000000000015872 000000000015996 000000000016120 000000000016244 000000000016368 000000000016492 000000000016616 000000000016740 000000000016864 000000000016988 000000000017112 000000000017236 000000000017360 000000000017484 000000000017608 000000000017732 000000000017856 000000000017980 000000000018104 000000000018228 000000000018352 000000000018476 000000000018600 000000000018724 000000000018848 000000000018972 000000000019096 000000000019220 000000000019344 000000000019468 000000000019592 000000000019716 000000000019840 000000000019964 000000000020088 000000000020212 000000000020336 000000000020460 000000000020584 000000000020708 000000000020832 000000000020956 000000000021080 000000000021204 000000000021328 000000000021452 000000000021576 000000000021700 000000000021824 000000000021948 000000000022072 000000000022196 000000000022320 000000000022444 000000000022568 000000000022692 000000000022816 000000000022940 000000000023064 000000000023188 000000000023312 000000000023436 000000000023560 000000000023684 000000000023808 000000000023932 000000000024056 000000000024180 000000000024304 000000000024428 000000000024552 000000000024676 000000000024800 000000000024924 000000000025048 000000000025172 000000000025296 000000000025420 000000000025544 000000000025668 000000000025792 000000000025916 000000000026040 000000000026164 000000000026288 000000000026412 000000000026536 000000000026660 000000000026784 000000000026908 000000000027032 000000000027156 000000000027280 000000000027404 000000000027528 000000000027652 000000000027776 000000000027900 000000000028024 000000000028148 000000000028272 000000000028396 000000000028520 000000000028644 000000000028768 000000000028892 000000000029016 000000000029140 000000000029264 000000000029388 000000000029512 000000000029636 000000000029760 000000000029884 000000000030008 000000000030132 000000000030256 000000000030380 000000000030504 000000000030628 000000000030752 000000000030876 000000000031000 000000000031124 000000000031248 000000000031372 000000000031496 000000000031620 000000000031744 000000000031868 000000000031992 000000000032116 000000000032240 … |
|
The digital expansion of the inverse of
999,999,999,999,999,999,999,876 produces a sequence of digits showing the
powers of 124, beginning with 1240, written in 24 digit
strings. The first 25 terms are
accurate.
1/999999999999999999999876 =
0.
000000000000000000000001 000000000000000000000124 000000000000000000015376 000000000000000001906624 000000000000000236421376 000000000000029316250624 000000000003635215077376 000000000450766669594624 000000055895067029733376 000006930988311686938624 000859442550649180389376 106570876280498368282637 214788658781797667047014 … |
|
The digital expansion of the inverse of
999,999,998,999,999,997,999,999,996 produces a digit sequence that shows the
terms of a Fibonacci like sequence (Tribonacci 1,2,4): a(0) = a(1) = 0, a(2)
= 1, and when n>2 then a(n) = 1*a(n-1) + 2*a(n-2) + 4*a(n-3). The terms are separated by spaces to make
reading them easier.
1/999999998999999997999999996 =
0.
000000000 000000000 000000001 000000001 000000003 000000009 000000019 000000049 000000123 000000297 000000739 000001825 000004491 000011097 000027379 000067537 000166683 000411273 001014787 002504065 006178731 015246009 037619731 092826673 229050171 … |
No comments:
Post a Comment