510 is apparently a size of vape battery
511 - the number you can call in the US and Canada for traffic information
Excluding reflections and color swaps, the number of arrangements of 10 beads, 2 of each of five colors, on a string (513)
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五一四 (wǔ yao sì) — 514: I want to die!
The number of sets of distinct positive integers such that the largest is 48, and the geometric mean of the set is an integer](A082553 - OEIS) (519)
The geometric mean of a set of n numbers is the nth root of the product of the numbers.
According to Angelology, the number 516 represents your guardian angels trying to communicate to you.
oops… skipped 515!
The number of inversion sequences of length 6 which avoid the pattern 120 (515)
An inversion sequence is basically a log of a bubble sort to correct a permutation.
Do the sorting for the largest value first, but record it right to left.
For example, the permutation 654321 will require 5 bubbles to move the six to the right, then four for the 5, three for the four, two for the three, one for the two, and none for the 1, leading to the inversion 012345.
An inversion contains a pattern if any ordered subset of the permutation matches the ordering of the pattern.
the list
This list is sorted according the the permutation, not the inversion sequence.
000000 000003 000021 010043 010141 010135 001311 002144 012211 012145
010000 010003 010021 010034 000221 010144 002211 002145 011121 011222
001000 000004 000031 010035 000321 010145 001121 001222 012121 011322
002000 000005 000041 010044 000331 000222 002121 001322 011131 011232
011000 010004 010031 010045 010221 000322 001131 001232 011141 011242
000100 010005 010041 001022 010321 000232 001141 001242 011221 011332
010100 001003 001021 002022 010331 000242 001221 001332 011321 011223
000200 002003 002021 001032 000112 000332 001321 001223 011331 011323
000300 001004 001031 001042 010112 000223 001331 001323 012221 011224
001100 001005 001041 002032 000212 000323 002221 001224 011112 011225
002100 002004 011021 002042 000312 000224 001112 001225 012112 011324
002200 002005 011031 001023 010212 000225 002112 001324 011212 011325
011100 011003 011041 002023 010312 000324 001212 001325 011312 011233
000010 011004 000012 001024 000113 000325 001312 001233 012212 011243
010010 011005 010012 001025 010113 000233 002212 001243 011113 011234
001010 000102 001012 002024 000114 000243 001113 001234 012113 011235
002010 010102 002012 002025 000115 000234 002113 001235 011114 011244
011010 000202 011012 001033 010114 000235 001114 001244 011115 011245
000020 000302 000013 001043 010115 000244 001115 001245 012114 011333
000030 000103 010013 001034 000213 000245 002114 001333 012115 011343
000040 010103 000014 001035 000313 000333 002115 001343 011213 011334
002020 000104 000015 001044 000214 000343 001213 001334 011313 011335
000110 000105 010014 001045 000215 000334 001313 001335 011214 011344
010110 010104 010015 002033 000314 000335 001214 001344 011215 011345
000210 010105 001013 002043 000315 000344 001215 001345 011314 012222
000310 000203 002013 002034 010213 000345 001314 002222 011315 012322
000220 000303 001014 002035 010313 010222 001315 002322 012213 012232
000320 000204 001015 002044 010214 010322 002213 002232 012214 012242
000330 000205 002014 002045 010215 010232 002214 002242 012215 012332
001110 000304 002015 011022 010314 010242 002215 002332 011122 012223
002110 000305 011013 011032 010315 010332 001122 002223 012122 012323
002210 001102 011014 011042 000122 010223 002122 002323 011132 012224
002220 002102 011015 011023 010122 010323 001132 002224 011142 012225
011110 002202 000022 011024 000132 010224 001142 002225 012132 012324
000001 001103 010022 011025 000142 010225 002132 002324 012142 012325
010001 002103 000032 011033 010132 010324 002142 002325 011123 012233
001001 001104 000042 011043 010142 010325 001123 002233 012123 012243
002001 001105 010032 011034 000123 010233 002123 002243 011124 012234
011001 002104 010042 011035 010123 010243 001124 002234 011125 012235
000101 002105 000023 011044 000124 010234 001125 002235 012124 012244
010101 002203 010023 011045 000125 010235 002124 002244 012125 012245
000201 002204 000024 000111 010124 010244 002125 002245 011133 012333
000301 002205 000025 010111 010125 010245 001133 002333 011143 012343
001101 011102 010024 000211 000133 010333 001143 002343 011134 012334
002101 011103 010025 000311 000143 010343 001134 002334 011135 012335
002201 011104 000033 010211 000134 010334 001135 002335 011144 012344
011101 011105 000043 010311 000135 010335 001144 002344 011145 012345
000002 000011 000034 000121 000144 010344 001145 002345 012133
010002 010011 000035 010121 000145 010345 002133 011111 012143
001002 001011 000044 000131 010133 001111 002143 012111 012134
002002 002011 000045 000141 010143 002111 002134 011211 012135
011002 011011 010033 010131 010134 001211 002135 011311 012144
Next will be 517.
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The other odd (and not prime) number skipped by @GeeTwo when he posted a unique way to count the number 519 skipping over 4 other numbers in the process. (517)
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The value of n in the largest known prime of the form n!!+1 (518)
That prime number
in 60 digit chunks
27292700363959435810002233046840403515711143297522176
254493187963159951866236199864149795040319209730962462959988
333729220819970503262237200907053049477006408745869015435984
923392452039418797622436743184684505000490799272015605244007
772883901083308080168589299247170935855131379401666365054006
064847093449510921200283680212107783652218341605326244616286
533003609895612179553401315004540862769913516111673921407236
874805796051534076120035827949909125871733483884215847509202
054724603789039510314304330920500798294679849390145798144000
000000000000000000000000000000000000000000000000000000000001
OBTW, @wgorgen, 517=11*47.
But 517 is the number of double palindrome structures of length 12 using exactly 2 different symbols (A284877 - OEIS) .
A double palindrome is the concatenation of two palindromes. Permuting (in this case swapping) the symbols will not change the structure. Valid palindromes include both the empty word and a singleton symbol.
I already got 519, so on to 520!
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130 times the number of posts that got messed up by GeeTwo skipping to 519 (4) equals 520
521 is the country code for mobile phones in Mexico. Originally, the country code was 52, but 521 was created due to a lack of 52 numbers.
The number of series-parallel networks with 8 unlabeled edges (522)
Also, the smallest such that (for n edges) the number is greater than 2^{n+1}.
The 523rd entry into the National Recording Registry according to that specific instance of Wikipedia, was the album Concert in the Garden by Maria Schneider. It won the 2005 Grammy for Best Large Jazz Ensemble Album.
You can listen to the album on her website
The number of ON cells in the 12th stage of growth of 2-d cellular automaton defined by “Rule 1” based on the 5-celled von Neumann neighborhood (524)
The active area for the automaton begins as a single ON cell. The area grows by one cell on each of the four sides, and the rule is: in the previous stage, were all five cells including myself and the four edge-adjacent to me OFF? The number of cells at stage n is 1 if n is even, (2n+1)^2-5 if odd.
