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hex numbers
Hex (also centered hexagonal) numbers are figurate numbers (see picture aside) defined as  $H_n=3n(n-1)+1$.

Three formulas involving hex numbers:

\[\sum_{n=1}^{\infty}\frac{1}{H_n}=\frac{\pi  \tanh \left(\frac{\pi}{2 \sqrt{3}}\right)}{\sqrt{3}}\,,\quad%
\sum_{n=1}^{\infty}\frac{H_n}{2^n}=13%
\quad\mbox{and}\quad\sum_{n=0}^{\infty}\frac{H_n}{n!}=4e\,.
\]

The first hex numbers are 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261 more terms

Hex numbers can also be... (you may click on names or numbers and on + to get more values)

a-pointer 631 1801 9241 + 9930310867 aban 19 37 61 + 995074000207 Achilles 12172437058327 alt.fact. 19 alternating 61 127 169 + 985818769 amenable 37 61 169 + 999899377 apocalyptic 1141 1261 2269 + 29701 arithmetic 19 37 61 + 9997351 balanced p. 22447 35317 45757 + 9974545747 binomial 91 8911 873181 + 821574197731 brilliant 169 817 1027 + 998038081 c.decagonal 61 3781 234361 + 214426605350161 c.heptagonal 547 368551 248402701 + 112842888508351 c.nonagonal 91 8911 873181 + 80505887094361 c.octagonal 169 32761 6355441 + 46399815451081 c.pentagonal 331 159391 76825981 + 17848365484951 c.square 61 5941 582121 + 53670591396241 c.triangular 19 631 21421 + 32919051946411 Carmichael 8911 172081 7995169 + 50886982081 Chen 19 37 127 + 97179517 congruent 37 61 127 + 9997351 Cunningham 37 127 217 + 9994070595601 cyclic 19 37 61 + 9997351 d-powerful 4447 22447 23497 + 9682237 de Polignac 127 331 1657 + 99930637 decagonal 1387 42127 52204237 + 59665447746451 deceptive 91 3367 8911 + 97144387957 deficient 19 37 61 + 9997351 dig.balanced 19 37 169 + 199389769 Duffinian 169 217 469 + 9986401 economical 19 37 61 + 19945987 emirp 37 1657 3169 + 199145269 emirpimes 169 817 1027 + 99965269 equidigital 19 37 61 + 19945987 eRAP 176530075057 esthetic 1234567 evil 169 469 547 + 999789841 fibodiv 19 61 29107 Friedman 127 32761 166381 902557 frugal 32761 148519 1951327 + 680817481 gapful 3367 64387 90307 + 99963102421 good prime 37 127 331 + 169989769 happy 19 91 331 + 9975457 Harshad 1141 1387 3781 + 9936180151 heptagonal 469 3367 226051 + 181728138938347 hexagonal 91 8911 873181 + 80505887094361 hoax 5544721 6872047 31076227 + 93057991 Hogben 91 1261 17557 + 346332937450507 Honaker 126691 333667 436627 + 972162007 house 271 iban 127 217 271 + 724717 idoneal 37 inconsummate 4219 32137 115837 + 841111 interprime 217 7957 12871 + 99308287 junction 721 919 2107 + 99584647 katadrome 61 91 631 + 876421 Lehmer 91 1141 1261 + 980322013567 Lucas 3571 lucky 37 127 169 + 9975457 m-pointer 61 magic 14911 magnanimous 61 metadrome 19 37 127 + 1234567 modest 19 721 1027 + 1807002919 Moran 1141 1387 3781 + 92524087 Motzkin 127 nialpdrome 61 91 331 + 87766666663321 nonagonal 12871 486019 5847005269 220785839821 nude 1771777 oban 19 37 397 + 919 odious 19 37 61 + 999899377 Ormiston 2784997 2967091 3069397 + 1979851231 palindromic 919 1081801 1188811 + 131374494473131 palprime 919 pancake 37 631 3571 + 558119378907721 panconsummate 37 61 91 + 721 pandigital 19 2252467 3124261 + 13337317 pentagonal 7957 1185037 10596309577 1578130224697 pernicious 19 37 61 + 9953587 persistent 11342506897 13946150827 14528930617 + 97368012541 Pierpont 19 37 plaindrome 19 37 127 + 133333366666669 Poulet 1387 4681 7957 + 916540502502241 power 169 32761 6355441 + 46399815451081 powerful 169 32761 6355441 + 46399815451081 prime 19 37 61 + 999962694781 primeval 37 repfigit 19 61 repunit 91 127 1261 + 346332937450507 Ruth-Aaron 2107 65211679981 self 547 817 2437 + 998366419 self-describing 22154133413419 semiprime 91 169 217 + 99965269 sphenic 3367 4921 8911 + 99999907 square 169 32761 6355441 + 46399815451081 star 37 1261 42841 + 65838103892821 straight-line 1234567 strobogrammatic 1081801 1188811 strong prime 37 127 331 + 99896011 super-d 19 127 169 + 9964519 taxicab 195841 684019 5318677 + 980590370647771 triangular 91 8911 873181 + 80505887094361 truncatable prime 37 397 547 + 93626947 twin 19 61 271 + 995304031 uban 19 37 61 + 75000075000019 Ulam 1387 9577 9919 + 9975457 undulating 919 upside-down 19 37 91 wasteful 91 721 817 + 9997351 weak prime 19 61 271 + 98756719 weakly prime 4103337817 Wieferich 7651 Zeisel 353977 2268651612169 zygodrome 1188811 2200777 661166611 + 552299998822111