A275413 a(0)=0 and a(n) is the smallest available integer not yet present in the sequence that starts with the last digit of a(n-1) augmented by 1.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 30, 13, 40, 14, 50, 15, 60, 16, 70, 17, 80, 18, 90, 19, 100, 101, 21, 22, 31, 23, 41, 24, 51, 25, 61, 26, 71, 27, 81, 28, 91, 29, 102, 32, 33, 42, 34, 52, 35, 62, 36, 72, 37, 82, 38, 92, 39, 103, 43, 44, 53, 45, 63, 46, 73, 47, 83, 48, 93, 49, 104, 54, 55, 64, 56, 74, 57, 84, 58, 94, 59, 105, 65, 66, 75, 67, 85, 68, 95, 69, 106, 76, 77, 86, 78, 96, 79, 107, 87, 88, 97, 89, 108, 98, 99, 109, 1000, 110, 111, 200, 112, 300

Offset

0,3

Comments

The sequence is a permutation of the nonnegative integers A001477.

Links

Table of n, a(n) for n=0..115.

Example

After [0,1,2,3,4,5,6,7,8,9,10] the next term must start with [0+1 = 1]; as 1 and 10 are already in the sequence, “11”, the smallest available integer, is chosen. The next term must start with [1+1 = 2]; as 2 is already in the sequence, “20” is chosen. The next term must start with [0+1 = 1]; as 1, 10 and 11 are already in the sequence, “12” is chosen. Etc.

Mathematica

a[1]=0; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[s=Array[a, n-1], k]||(g=1+Mod[a[n-1], 10]; FromDigits[IntegerDigits[k][[;; IntegerLength@g]]]!=g), k++]; k]; Array[a, 116] (* Giorgos Kalogeropoulos, May 13 2022 *)

Crossrefs

Sequence in context: A332144 A339018 A303948 * A273376 A247758 A247757

Adjacent sequences: A275410 A275411 A275412 * A275414 A275415 A275416

Keyword

nonn,base

Author

Eric Angelini, Jul 27 2016

Status

approved