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alternating numbers
A number is alternating in base  $b$  if in its representation odd and even digits alternate.

It is easy to verify that up to  $10^n$  there are exactly  $1+9\cdot(5^n-1)/4$  alternating numbers in base 10.

The first alternating numbers in base 10 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 101 more terms

Below, the spiral pattern of alternating numbers up to 6400. See the page on prime numbers for an explanation and links to similar pictures.

spiral pattern of alternating numbers

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

a-pointer 101 103 181 + 89892169 ABA 18 32 50 + 896761250 aban 10 12 14 + 989 abundant 12 18 30 + 49896945 Achilles 72 432 3456 + 981418707 admirable 12 30 54 + 98989854 alt.fact. 101 amenable 12 16 21 + 989898989 amicable 1210 503056 1438983 + 856305272 apocalyptic 218 278 361 + 29898 arithmetic 14 21 23 + 9898989 astonishing 27 216 3078 + 23490 automorphic 25 76 balanced p. 563 947 2903 + 989892367 Bell 52 bemirp 109698961 169896901 betrothed 1050 16587 binomial 10 21 36 + 985036305 brilliant 10 14 21 + 989898769 c.decagonal 61 101 361 + 989472781 c.heptagonal 43 547 638 + 967658147 c.nonagonal 10 325 496 + 969694741 c.octagonal 25 49 81 + 987656329 c.pentagonal 16 76 141 + 989676781 c.square 25 41 61 + 987412361 c.triangular 10 85 109 + 989232121 cake 232 470 834 + 494561274 Canada 125 581 8549 Carmichael 561 10585 278545 + 547652161 Carol 47 16127 Catalan 14 1430 Chen 23 29 41 + 89898929 congruent 14 21 23 + 9898989 constructible 10 12 16 + 69632 cube 27 125 216 + 381078125 Cullen 25 65 161 385 Cunningham 10 50 63 + 987090725 Curzon 14 18 21 + 189898965 cyclic 23 29 41 + 9898985 D-number 21 63 69 + 7038723 d-powerful 43 63 89 + 898729 de Polignac 127 149 509 + 89898941 decagonal 10 27 52 + 876589252 deceptive 703 2981 4141 + 963018721 deficient 10 14 16 + 9898989 dig.balanced 10 12 21 + 189898989 double fact. 105 945 droll 72 672 12189696 + 270729216 Duffinian 16 21 25 + 9898987 eban 30 32 34 + 56 economical 10 14 16 + 18989878 emirp 107 149 167 + 189898781 emirpimes 49 58 85 + 98989678 enlightened 250 256 equidigital 10 14 16 + 18989878 eRAP 98 1274 3438 + 985270783 esthetic 10 12 21 + 989898989 Eulerian 16369 evil 10 12 18 + 989898989 fibodiv 14 47 61 + 65454505 Fibonacci 21 34 89 + 6765 Friedman 25 121 125 + 983250 frugal 125 256 343 + 989870105 gapful 105 121 143 + 989898765 Gilda 29 49 78 65676 Giuga 30 858 good prime 29 41 67 + 189834389 happy 10 23 32 + 9898921 harmonic 270 496 672 1638 Harshad 10 12 18 + 989898909 heptagonal 18 34 81 + 989298783 hex 61 127 169 + 985818769 hexagonal 45 276 325 + 985036305 highly composite 12 36 hoax 58 85 94 + 98987212 Hogben 21 43 183 + 981036363 Honaker 2141 2707 2729 + 989252101 house 32 78 434 + 50521016 hungry 74 hyperperfect 21 301 325 + 569450701 iban 10 12 14 + 747474 iccanobiF 836 idoneal 10 12 16 + 385 impolite 16 32 256 inconsummate 63 65 161 + 989892 interprime 12 18 21 + 98989896 Jacobsthal 21 43 85 + 10923 Jordan-Polya 12 16 32 + 147456 junction 101 103 105 + 98989058 Kaprekar 45 703 5050 + 909090909 katadrome 10 21 30 + 987654321 Kynea 23 Lehmer 85 561 703 + 989438341 Leyland 32 54 145 + 69632 lonely 23 38501 1272749 Lucas 18 29 47 + 3010349 lucky 21 25 43 + 9898927 Lynch-Bell 12 36 216 + 981432 m-pointer 23 61 magic 34 65 369 + 727210385 magnanimous 12 14 16 + 101 metadrome 12 14 16 + 123456789 modest 23 29 49 + 989696969 Moran 18 21 27 + 98989074 Motzkin 21 127 323 narcissistic 1634 9474 92727 nialpdrome 10 21 30 + 987654321 nonagonal 325 474 856 + 987092541 nude 12 36 212 + 498989232 O'Halloran 12 36 oban 10 12 16 + 989 octagonal 21 65 96 + 947816325 odious 14 16 21 + 989898985 Ormiston 250109 276781 456329 + 989696341 palindromic 101 121 141 + 989898989 palprime 101 181 383 + 989898989 pancake 16 29 56 + 989212961 panconsummate 10 12 14 + 721 pandigital 21 78 141 + 298989892 partition 30 56 101 + 10143 pentagonal 12 70 92 + 963616901 perfect 496 pernicious 10 12 14 + 9898985 Perrin 10 12 29 + 76725 Pierpont 109 163 769 10369 plaindrome 12 14 16 + 123456789 Poulet 341 561 2701 + 967270129 power 16 25 27 + 987656329 powerful 16 25 27 + 987656329 practical 12 16 18 + 8989890 prim.abundant 12 18 30 + 98989854 prime 23 29 41 + 989898989 primeval 107 10123 10367 + 101234567 primorial 30 210 pronic 12 30 56 + 892187030 Proth 25 41 49 + 989036545 pseudoperfect 12 18 30 + 989898 rare 65 repfigit 14 47 61 repunit 21 43 63 + 981036363 Rhonda 5832 12985 185614 + 927492925 Ruth-Aaron 16 25 49 + 987012585 Sastry 183 self 121 143 165 + 989898969 semiprime 10 14 21 + 98989834 sliding 25 29 52 + 490329250 Smith 27 58 85 + 98987250 sphenic 30 70 78 + 98989894 square 16 25 36 + 987656329 star 121 181 541 + 967054321 straight-line 123 147 210 + 987654321 strobogrammatic 69 96 101 + 818181818 strong prime 29 41 67 + 89898947 subfactorial 1854 super Niven 10 12 30 + 909090 super-d 69 81 105 + 9898981 superabundant 12 36 tau 12 18 36 + 949810761 taxicab 216125 5832729 10589696 + 414723456 tetrahedral 10 56 165 + 890169874 tetranacci 29 56 1490 triangular 10 21 36 + 985036305 tribonacci 81 149 274 927 trimorphic 25 49 76 + 749 truncatable prime 23 29 43 + 929636947 twin 29 41 43 + 989894749 uban 10 12 16 + 98 Ulam 16 18 36 + 9898545 undulating 101 121 141 + 989898989 unprimeable 325 890 892 + 9898985 untouchable 52 96 210 + 989896 upside-down 258 456 654 + 989852121 vampire 2187 105210 329656 + 58703472 wasteful 12 18 30 + 9898989 weak prime 23 43 47 + 89898983 weakly prime 81434501 85478369 123892907 + 983810701 weird 70 836 5830 + 987490 Wieferich 298389 410787 1232361 Woodall 23 63 323 + 1214 Zeisel 105 4505 1012121 781296905 Zuckerman 12 36 212 + 832761216 Zumkeller 12 30 54 + 96525