A138141 Numbers with digits in ascending order that differ exactly by 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 23, 34, 45, 56, 67, 78, 89, 123, 234, 345, 456, 567, 678, 789, 1234, 2345, 3456, 4567, 5678, 6789, 12345, 23456, 34567, 45678, 56789, 123456, 234567, 345678, 456789, 1234567, 2345678, 3456789, 12345678, 23456789, 123456789

Offset: 1

Author

Omar E. Pol, Mar 19 2008

Keywords

• base
• easy
• fini
• full
• nonn

Comments

This finite sequence has 45 members. The last member is 123456789. There are 10-k members with k digits. See A052017 for primes in this sequence. All members with 3 or more digits are straight-line numbers A135643.

Crossrefs

Cf. A052017, A059043, A135643, A138142.

Programs

Mathematica

Table[FromDigits/@Partition[Range[9],n,1],{n,9}]//Flatten (* Harvey P. Dale, Mar 19 2017 *)

Formula

a(n) = floor(((9*t^2 - 189*t + 18*n + 182) * (10^t - 1) - 18*t) / 162), where t = floor((21 - sqrt(369 - 8*n)) / 2). - Christopher J. Thomas, Feb 14 2024