A290950 Positive integers whose digits are in increasing order and whose successive digits differ by exactly 2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 24, 35, 46, 57, 68, 79, 135, 246, 357, 468, 579, 1357, 2468, 3579, 13579

Offset

1,2

Comments

There are 11 - 2*k terms of the sequence with k digits, 1 <= k <= 5.

Links

Table of n, a(n) for n=1..25.

Formula

The terms can be described by the following linear equations:

for 1 <= n <= 9, a(n) = n;

for 10 <= n <= 16, a(n) = 11*(n - 9) + 2;

for 17 <= n <= 21, a(n) = 111*(n - 16) + 24;

for 22 <= n <= 24, a(n) = 1111*(n - 21) + 246;

for n = 25, a(n) = 11111*(n - 24) + 2468.

Mathematica

Select[Range[10^5], Or[Length@ # == 1, Union@ Differences@ # == {2}] &@ IntegerDigits@ # &] (* Michael De Vlieger, Aug 15 2017 *)

Crossrefs

Sequence in context: A034294 A304246 A271837 * A032577 A244155 A066310

Adjacent sequences: A290947 A290948 A290949 * A290951 A290952 A290953

Keyword

nonn,base,fini,full

Author

Enrique Navarrete, Aug 14 2017

Status

approved