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centered heptagonal numbers
Centered heptagonal numbers are figurate numbers (see picture aside) defined as  $H_n=7n(n-1)/2+1$.

Two formulas involving centered heptagonal numbers:

\[\sum_{n=1}^{\infty}\frac{1}{H_n}=\frac{2 \pi  \tanh \left(\frac{\pi
   }{2 \sqrt{7}}\right)}{\sqrt{7}}%
\quad\mbox{and}\quad\sum_{n=1}^{\infty}\frac{H_n}{2^n}=15\,.
\]

The first centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331 more terms

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

a-pointer 1933 41203 114031 + 8922870503 ABA 512072 33035808968 aban 22 43 71 + 999495000547 abundant 736 3256 7568 + 49022072 Achilles 512072 33035808968 2414198307851 alternating 43 547 638 + 967658147 amenable 148 197 253 + 999930772 apocalyptic 841 1772 1933 + 29947 arithmetic 22 43 71 + 9978613 balanced p. 176401 890821 1545461 + 9583951693 binomial 253 64261 16322041 + 1053000152821 brilliant 253 841 26797 + 999694151 c.decagonal 2101 265651 529471951 + 133427990609551 c.nonagonal 253 64261 16322041 + 267457893082381 c.octagonal 841 755161 678133681 + 546848356574521 c.pentagonal 106 15016 2132131 + 866724458635141 c.square 841 43513 54236113 + 181102250526121 c.triangular 316 7246 3818431 + 558871623400861 Carmichael 29020321 127664461 Chen 71 197 953 + 99785911 congruent 22 71 148 + 9978613 cube 1331 Cunningham 197 7568 176401 + 127740041301797 Curzon 386 638 953 + 193035158 cyclic 43 71 197 + 9978613 d-powerful 43 463 2843 + 9442322 de Polignac 2843 3697 4663 + 99823291 decagonal 19951 962851 16088702701 776445148501 deceptive 5461 29020321 107556373 + 8314386011 deficient 22 43 71 + 9990436 dig.balanced 197 316 841 + 199852423 Duffinian 253 841 1331 + 9966797 economical 43 71 106 + 19967263 emirp 71 953 1471 + 198954211 emirpimes 2458 3046 3473 + 99972881 equidigital 43 71 106 + 19967263 esthetic 43 2101 evil 43 71 106 + 999930772 Friedman 736 31256 46691 + 512072 frugal 1331 1806848 2339072 + 678133681 gapful 253 1331 24403 + 99842279272 good prime 71 2647 50821 + 145857181 happy 386 638 736 + 9931391 Harshad 736 19426 36058 + 9998597533 heptagonal 148 21022 2984983 + 8545594544488 hex 547 368551 248402701 + 112842888508351 hexagonal 16322041 4145734153 hoax 22 3046 13672 + 99599116 Hogben 43 463 38221 + 300797044280503 Honaker 1933 5741 11173 + 980855191 hyperperfect 833857593493 iban 22 43 71 + 742211 idoneal 22 253 inconsummate 386 2276 3046 + 970208 interprime 386 736 8926 + 96487126 Jacobsthal 43 5461 junction 3928 6931 10018 + 99524447 katadrome 43 71 841 953 Lehmer 4411 5461 19951 + 839844151147 lucky 43 463 841 + 9731947 magnanimous 43 316 736 + 1772 metadrome 148 2458 modest 1618 1933 10018 + 1950433948 Moran 19426 105358 1801822 + 95716846 nialpdrome 22 43 71 + 83333321 nude 22 811448 12882248 22111888 oban 316 386 638 + 953 octagonal 736 5461 496133 + 151906034826008 odious 22 148 253 + 999575851 Ormiston 18397 114031 654697 + 1841290613 palindromic 22 1331 1919191 + 38437311373483 pancake 22 106 5461 + 111528538797061 panconsummate 43 pandigital 94986116 104550916 108762676 + 229946956 partition 22 pentagonal 22 11572 265651 + 38881099834501 pernicious 22 148 253 + 9978613 Perrin 22 persistent 10892467538 16450937728 19286104573 + 93207845186 plaindrome 22 148 2458 Poulet 5461 19951 49981 + 180154037487061 power 841 1331 755161 + 608963290321 powerful 841 1331 512072 + 546848356574521 practical 736 3256 7568 + 9304856 prim.abundant 477856 1199836 2507968 + 19386368 prime 43 71 197 + 999977610703 pseudoperfect 736 3256 7568 + 866272 repdigit 22 repfigit 197 repunit 43 463 5461 + 300797044280503 Ruth-Aaron 1331 3388610191 4492383358 self 547 1772 4663 + 999220993 self-describing 22 semiprime 22 106 253 + 99972881 Smith 22 3046 24403 + 99263326 sphenic 638 4922 6322 + 99860678 square 841 755161 678133681 + 546848356574521 star 253 14113 3063061 + 448314542426521 strong prime 71 197 1471 + 99823291 super-d 106 1072 1331 + 9990436 tau 3928 8576 13672 + 993315968 triangular 253 64261 16322041 + 267457893082381 truncatable prime 43 71 197 + 9283 twin 43 71 197 + 990252271 uban 22 43 71 + 56000098000043 Ulam 106 148 197 + 9919603 undulating 1919191 unprimeable 1072 4166 4922 + 9990436 untouchable 7568 11572 30598 + 999916 upside-down 3175397 3695147 96119941 + 77519519533 vampire 3074749861 wasteful 22 148 253 + 9990436 weak prime 43 463 547 + 99673813 weakly prime 9545528833 Zumkeller 736 3256 7568 + 74096 zygodrome 22 4411 669922 + 11662266115522