A337843 a(n) is n + the number of digits in the decimal expansion of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset: 0

Author

Jaroslav Krizek, Sep 25 2020

Keywords

• nonn
• base

Comments

a(n) is an increasing injective sequence that is not surjective.

a(n) is also the sequence of numbers m that can be written as (m + number of digits of m) for some m >= 0, complement of numbers from A081552(n) for n > 1.

Sequence is not the same as A101947, first different term is a(77) = 79.

Examples

			a(10) = 10 + 2 = 12.
		

Crossrefs

Cf. A055642, A062028, A081552, A230099.

Cf. A110803 (n * the number of digits in the decimal expansion of n).

Programs

Magma

[1] cat [n + #Intseq(n): n in [1..100]];

Mathematica

a[0] = 1; a[n_] := n + IntegerLength[n]; Array[a, 100, 0] (* Amiram Eldar, Sep 25 2020 *)

PARI

a(n) = if (n==0, 1, n + #digits(n)); \\ Michel Marcus, Sep 26 2020

Formula

a(n) = n + A055642(n).