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iban numbers
A number  $n$  is called iban if its name (in English) does not contain the letter "i".

Assuming that the name of every power of 10 greater than  $10^5$  ends in "-illion" (like million, billion, trillion, etc.), then the iban numbers are finite. Counting 0 (zero) there are 30276 of them, the largest begin 777777.

Iban numbers belong to the same family of aban numbers, eban numbers, oban numbers, and uban numbers. All quite boring, if I may speak my mind...

As for the above sets, the definition is not really precise, since large numbers may have non-standard names.

The first iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101 more terms

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

a-pointer 11 101 103 + 777317 ABA 24 72 200 + 744200 aban 10 11 12 + 777 abundant 12 20 24 + 777774 Achilles 72 200 1323 + 771147 admirable 12 20 24 + 777774 alt.fact. 101 4421 alternating 10 12 14 + 747474 amenable 12 17 20 + 777777 amicable 220 1210 10744 + 202444 anti-perfect 244 apocalyptic 220 222 224 + 27777 arithmetic 11 14 17 + 777777 astonishing 27 204 balanced p. 173 211 373 + 777103 Bell 203 4140 21147 betrothed 140 2024 binomial 10 20 21 + 742371 brilliant 10 14 21 + 774443 c.decagonal 11 101 211 + 774211 c.heptagonal 22 43 71 + 742211 c.nonagonal 10 703 1711 + 442270 c.octagonal 121 441 2401 + 741321 c.pentagonal 141 4101 7701 + 741201 c.square 41 221 421 + 770041 c.triangular 10 274 2110 + 772210 cake 42 470 3304 + 447720 Carmichael 41041 101101 410041 Carol 47 223 Catalan 14 42 Chen 11 17 23 + 777317 compositorial 24 congruent 14 20 21 + 777774 constructible 10 12 17 + 41120 cube 27 343 1000 + 343000 Cullen 10241 Cunningham 10 17 24 + 774401 Curzon 14 21 41 + 777714 cyclic 11 17 23 + 777773 D-number 21 111 123 + 777477 d-powerful 24 43 224 + 777322 de Polignac 127 373 701 + 777701 decagonal 10 27 370 + 714447 deceptive 703 4141 7471 + 420343 deficient 10 11 14 + 777777 dig.balanced 10 11 12 + 777744 droll 72 240 2240 4224 Duffinian 21 27 77 + 777773 eban 40 42 44 + 44044 economical 10 11 14 + 777743 emirp 17 71 73 + 777421 emirpimes 122 123 143 + 777721 enlightened 2304 2744 equidigital 10 11 14 + 777743 eRAP 20 24 170 + 220124 esthetic 10 12 21 + 343212 Eulerian 11 120 247 302 evil 10 12 17 + 777777 factorial 24 120 720 40320 fibodiv 14 47 122 + 100177 Fibonacci 21 144 377 17711 Friedman 121 127 343 + 774144 frugal 243 343 1024 + 777243 gapful 100 110 120 + 777777 Gilda 110 220 314 + 2207 Giuga 1722 good prime 11 17 41 + 747401 happy 10 23 44 + 777443 harmonic 140 270 Harshad 10 12 20 + 777770 heptagonal 112 342 403 + 747202 hex 127 217 271 + 724717 hexagonal 120 703 1770 + 717003 highly composite 12 24 120 + 720720 hoax 22 202 274 + 777417 Hogben 21 43 73 + 777043 Honaker 1301 2141 2221 + 773273 house 271 10470 23101 + 72447 hungry 17 74 144 + 712201 hyperperfect 21 301 2041 214273 iccanobiF 124 idoneal 10 12 21 + 1320 impolite 1024 inconsummate 173 272 371 + 777771 insolite 111 11112 interprime 12 21 42 + 777740 Jacobsthal 11 21 43 + 341 Jordan-Polya 12 24 72 + 414720 junction 101 103 107 + 777744 Kaprekar 703 2223 7272 + 22222 katadrome 10 20 21 + 743210 Kynea 23 4223 Lehmer 247 703 771 + 771001 Leyland 17 100 177 + 23401 lonely 23 120 211 + 370317 Lucas 11 47 123 + 271443 lucky 21 43 73 + 777777 Lynch-Bell 12 24 124 + 4172 m-pointer 23 1123 1321 + 27211 magic 111 4010 magnanimous 11 12 14 + 777712 metadrome 12 14 17 + 12347 modest 23 103 111 + 777777 Moran 21 27 42 + 777411 Motzkin 21 127 323 narcissistic 370 371 407 nialpdrome 10 11 20 + 777777 nonagonal 24 111 204 + 720271 nude 11 12 22 + 777777 O'Halloran 12 20 44 + 420 oban 10 11 12 + 777 octagonal 21 40 341 + 373121 odious 11 14 21 + 777774 Ormiston 240473 343373 447173 palindromic 11 22 44 + 777777 palprime 11 101 373 + 77477 pancake 11 22 121 + 773147 panconsummate 10 11 12 + 721 pandigital 11 21 114 + 774411 partition 11 22 42 + 147273 pentagonal 12 22 70 + 777240 pernicious 10 11 12 + 777774 Perrin 10 12 17 + 43721 Pierpont 17 73 plaindrome 11 12 14 + 777777 Poulet 341 2047 2701 + 722201 power 27 100 121 + 774400 powerful 27 72 100 + 774400 practical 12 20 24 + 777744 prim.abundant 12 20 42 + 777774 prime 11 17 23 + 777743 primeval 107 10123 102347 primorial 210 2310 pronic 12 20 42 + 777042 Proth 17 41 177 + 777217 pseudoperfect 12 20 24 + 777774 repdigit 11 22 44 + 777777 repfigit 14 47 742 1104 repunit 21 40 43 + 777043 Ruth-Aaron 24 77 104 + 773312 Saint-Exupery 2040 4200 43740 + 124320 self 20 42 110 + 777770 self-describing 22 4444 224444 + 444422 semiprime 10 14 21 + 777773 sliding 11 20 70 + 700000 Smith 22 27 121 + 777417 Sophie Germain 11 23 41 + 777173 sphenic 42 70 102 + 777774 square 100 121 144 + 774400 star 73 121 1441 + 720373 straight-line 111 123 147 + 777777 strobogrammatic 11 101 111 + 111111 strong prime 11 17 41 + 777473 subfactorial 44 super Niven 10 12 20 + 777000 super-d 107 127 247 + 777743 superabundant 12 24 120 + 720720 tau 12 24 40 + 777704 taxicab 4104 tetrahedral 10 20 120 + 410040 tetranacci 401 773 147312 triangular 10 21 120 + 742371 tribonacci 24 44 274 + 410744 trimorphic 24 truncatable prime 17 23 43 + 24373 twin 11 17 41 + 777421 uban 10 11 12 + 77 Ulam 11 47 72 + 777722 undulating 101 121 141 + 747474 unprimeable 200 204 320 + 777774 untouchable 120 124 210 + 777774 upside-down 73 3377 7373 vampire 174370 304717 wasteful 12 20 22 + 777777 weak prime 23 43 47 + 777743 weird 70 11410 12110 + 770210 Woodall 17 23 323 + 4373 Zeisel 24211 207177 Zuckerman 11 12 24 + 742112 Zumkeller 12 20 24 + 100000 zygodrome 11 22 44 + 777777