Search a number
straight-line numbers
A number  $n>99$  is said to be straight-line if its digits form an arithmetic progression.

For example, 123456 (step is 1), 666 (step is 0), or 7531 (step is -2).

While there are infinite straight-line numbers, only 96 of them are not repdigits, the largest being 9876543210.

The first straight-line numbers are 111, 123, 135, 147, 159, 210, 222, 234, 246, 258, 321, 333, 345, 357, 369, 420, 432, 444, 456, 468, 531, 543, 555, 567, 579, 630, 642, 654, 666, 678 more terms

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

A graph displaying how many straight-line numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of straight-line numbers
Useful links OEIS, Sequence A135643
Straight-line numbers can also be... (you may click on names or numbers and on + to get more values)

aban 111 123 135 + 999 abundant 210 222 234 + 12345678 Achilles 432 864 3456 admirable 222 234 246 + 678 alternating 123 147 210 + 987654321 amenable 321 333 345 + 987654321 apocalyptic 222 666 840 + 23456 arithmetic 111 123 135 + 9999999 binomial 210 630 666 741 brilliant 1357 56789 c.pentagonal 456 951 Chen 4567 23456789 congruent 111 135 159 + 9999999 Cunningham 840 999 7777 + 99999999999999 Curzon 210 321 345 + 33333333 cyclic 123 159 321 + 7654321 D-number 111 123 159 + 876543 d-powerful 135 333 357 + 876543 de Polignac 4567 98765 11111111 23456789 deceptive 7777 11111 1111111 + 11111111111 deficient 111 123 135 + 9999999 dig.balanced 135 147 210 + 66666666 Duffinian 111 333 543 + 7777777 economical 111 123 135 + 1234567 emirpimes 123 159 321 + 7654321 equidigital 111 123 135 + 1234567 esthetic 123 210 234 + 9876543210 evil 111 123 135 + 888888888 Fibonacci 987 Friedman 23456 234567 765432 gapful 135 1111 2222 + 9999999999 happy 888 3456 5555 + 9876543 Harshad 111 135 210 + 9876543210 heptagonal 13579 hex 1234567 hexagonal 630 highly composite 840 hoax 234 456 654 + 6666666 Hogben 111 iban 111 123 147 + 777777 idoneal 210 345 357 840 inconsummate 432 531 543 + 98765 insolite 111 111111111 interprime 111 246 420 + 543210 Jordan-Polya 432 864 3456 junction 111 210 420 + 22222222 Kaprekar 999 7777 9999 + 999999999999999 katadrome 210 321 420 + 9876543210 Lehmer 1111 Lucas 123 lucky 111 135 159 + 7777777 Lynch-Bell 135 432 864 magic 111 369 metadrome 123 135 147 + 123456789 modest 111 222 333 + 1111111111 Moran 111 222 333 + 12345 nialpdrome 111 210 222 + 999999999999999 nonagonal 111 6666 nude 111 135 222 + 444444444 O'Halloran 420 oban 333 357 369 + 999 odious 234 321 333 + 999999999 palindromic 111 222 333 + 999999999999999 pandigital 135 147 210 + 9876543210 partition 135 pentagonal 210 852 pernicious 234 258 321 + 7654321 persistent 9876543210 plaindrome 111 123 135 + 999999999999999 powerful 432 864 3456 practical 210 234 420 + 8765432 prim.abundant 222 246 258 + 999999 prime 4567 76543 23456789 primorial 210 pronic 210 420 Proth 321 pseudoperfect 210 222 234 + 999999 repdigit 111 222 333 + 999999999999999 repunit 111 1111 11111 + 111111111111111 Ruth-Aaron 369 self 222 345 468 + 555555555 self-describing 4444 666666 88888888 semiprime 111 123 159 + 7654321 Smith 654 666 852 + 98765432 sphenic 222 246 258 + 9876543 strobogrammatic 111 888 1111 + 888888888888888 super Niven 210 420 630 840 super-d 333 369 531 + 9876543 superabundant 840 tau 444 468 852 + 444444444 triangular 210 630 666 741 trimorphic 999 9999 99999 + 999999999999999 twin 76543 Ulam 258 456 864 + 9999999 unprimeable 840 5678 7654 + 8888888 untouchable 210 246 852 + 765432 upside-down 159 258 357 + 555555555555555 wasteful 210 222 234 + 9999999 weak prime 4567 76543 23456789 Woodall 159 99999999999 Zuckerman 111 135 432 + 1111111111 Zumkeller 210 222 234 + 87654 zygodrome 111 222 333 + 999999999999999