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centered decagonal numbers
Centered decagonal numbers are figurate numbers (see picture aside) defined as  $D_n=5n(n-1)+1$.

Three formulas involving centered decagonal numbers:

\[\sum_{n=1}^{\infty}\frac{1}{D_n}=\frac{\pi \tan \left(\frac{\pi }{2 \sqrt{5}}\right)}{\sqrt{5}}\,,\quad \sum_{n=0}^{\infty}\frac{D_n}{n!}=6e\,, \quad\mbox{and}\quad\sum_{n=1}^{\infty}\frac{D_n}{2^n}=21\,. \]

The first centered decagonal numbers are 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of centered decagonal numbers

A graph displaying how many centered decagonal numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of centered decagonal numbers
Useful links Wikipedia, Centered decagonal number
OEIS, Sequence A062786
Centered decagonal numbers can also be... (you may click on names or numbers and on + to get more values)

a-pointer 11 101 5281 + 9988438601 aban 11 31 61 + 998426000911 alt.fact. 101 alternating 61 101 361 + 989472781 amenable 61 101 281 + 999768701 apocalyptic 361 2101 2311 + 29261 arithmetic 11 31 61 + 9989911 balanced p. 211 20161 135301 + 9897022951 bemirp 1901 199068088111 binomial 1711 2467531 3558178261 5130890585101 brilliant 361 451 551 + 998637781 c.heptagonal 2101 265651 529471951 + 133427990609551 c.nonagonal 1711 2467531 3558178261 5130890585101 c.octagonal 361 116281 37442161 + 3882078149401 c.pentagonal 31 1051 35701 + 54865086577351 c.square 61 1201 87781 + 263205560604901 c.triangular 31 361 14851 + 801550501782031 Carmichael 2704801 392099401 1030401901 + 369309612001 Chen 11 31 101 + 99971561 congruent 31 61 101 + 9989911 Cunningham 31 101 32401 + 348305329443601 Curzon 281 1901 4061 + 189758801 cyclic 11 31 61 + 9989911 d-powerful 8201 249761 258781 + 4394531 de Polignac 5951 12251 15401 + 99837461 decagonal 451 145351 46802701 + 4852597686751 deceptive 451 67861 974611 + 15070324501 deficient 11 31 61 + 9989911 dig.balanced 11 551 661 + 197160601 Duffinian 361 451 551 + 9989911 economical 11 31 61 + 19990001 emirp 31 1201 1901 + 199364551 emirpimes 551 781 5611 + 99837461 equidigital 11 31 61 + 19990001 esthetic 101 2101 Eulerian 11 evil 101 281 1711 + 999910111 fibodiv 61 911 14311 frugal 119351 1987651 2122261 + 768862001 gapful 451 781 4961 + 79965084161 good prime 11 101 2531 + 167360051 happy 31 3001 5281 + 9863101 Harshad 3781 20801 50501 + 9715011601 heptagonal 1901737531 hex 61 3781 234361 + 214426605350161 hexagonal 2467531 5130890585101 hoax 361 9031 30811 + 98323951 Hogben 31 211 9901 + 729500152756861 Honaker 1361 6301 7411 + 995531051 iban 11 101 211 + 774211 inconsummate 3251 7031 8201 + 979031 interprime 40051 562801 1055701 + 98545801 Jacobsthal 11 junction 101 911 2311 + 99926851 katadrome 31 61 Lehmer 451 2761 5611 + 998291946961 lonely 211 Lucas 11 lucky 31 151 211 + 9779011 m-pointer 61 magnanimous 11 61 101 + 661 modest 211 911 17111 + 991020811 Moran 3781 50501 102961 + 94156301 nialpdrome 11 31 61 + 222222211111111 nonagonal 113740651 85504618351 nude 11 oban 11 911 octagonal 4961 19061281 73233437761 281362848817601 odious 11 31 61 + 999627301 Ormiston 4072531 6991531 11590031 + 1999100101 palindromic 11 101 151 + 155075181570551 palprime 11 101 151 + 107635959536701 pancake 11 211 781 + 910957680946951 panconsummate 11 31 61 + 661 pandigital 11 partition 11 101 pentagonal 265651 61716605501 pernicious 11 31 61 + 9989911 persistent 15208439761 24708692531 24869230751 + 92014786531 plaindrome 11 Poulet 2704801 4154161 5859031 + 248626476315361 power 361 116281 37442161 + 3882078149401 powerful 361 116281 37442161 + 3882078149401 prime 11 31 61 + 999995100781 repdigit 11 repfigit 61 repunit 31 211 781 + 729500152756861 Rhonda 15354942361 Ruth-Aaron 1027246111 self 31 211 80011 + 997790011 semiprime 361 451 551 + 99882151 sliding 11 101 Smith 9031 30811 34861 + 98323951 Sophie Germain 11 281 911 + 9892129601 sphenic 20801 22781 37411 + 99703451 square 361 116281 37442161 + 3882078149401 star 661 318781 153651961 + 35696730969901 strobogrammatic 11 101 strong prime 11 101 281 + 99971561 super-d 31 281 781 + 9975781 triangular 1711 2467531 3558178261 5130890585101 truncatable prime 31 twin 11 31 61 + 999768701 uban 11 31 61 + 81052016000051 Ulam 11 451 781 + 9947551 undulating 101 151 upside-down 9461 vampire 1209712351 wasteful 451 551 781 + 9989911 weak prime 31 61 151 + 99926851 weakly prime 3383250781 88540120561 94269493951 Wieferich 3511 Zuckerman 11 zygodrome 11 22111 445511 + 884441155522111