A281091 Numbers beginning and ending with their digital root in decimal representation.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 99, 181, 272, 363, 454, 545, 636, 727, 818, 909, 999, 1081, 1171, 1261, 1351, 1441, 1531, 1621, 1711, 1801, 1891, 1981, 2072, 2162, 2252, 2342, 2432, 2522, 2612, 2702, 2792, 2882, 2972, 3063, 3153, 3243, 3333, 3423, 3513, 3603, 3693, 3783, 3873, 3963, 4054, 4144, 4234, 4324, 4414

Offset

1,3

Comments

1% of the nonnegative integers are in the sequence, approximatively.

Up to 10^k there are exactly 1 + (10^k + 800)/90 terms. - Giovanni Resta, Apr 12 2017

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

The digital root of 99 is 9 and "9" is the first and last digit of "99", so 99 is in the sequence.
The digital root of 100 is 1 and "1" is not the last digit of "100", so 100 is not in the sequence.
The digital root of 181 is 1 and "1" is the first and last digit of "181", so 181 is in the sequence.
Etc.

Mathematica

{0} ~ Join ~ Select[Range[10^4], IntegerDigits[#][[{1, -1}]] == {1, 1} (Mod[#-1, 9] + 1) &] (* Giovanni Resta, Apr 12 2017 *)

Crossrefs

Sequence in context: A066492 A348834 A342978 * A271569 A239138 A345964

Adjacent sequences: A281088 A281089 A281090 * A281092 A281093 A281094

Keyword

nonn,base,easy

Author

Eric Angelini and Jean-Marc Falcoz, Apr 12 2017

Status

approved