A001637 Numbers with an even number of digits.

10, 11, 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, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 1000, 1001

Offset

1,1

Comments

The lower and upper asymptotic densities of this sequence are 1/11 and 10/11, respectively. - Amiram Eldar, Feb 01 2021

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

A055642(a(n)) mod 2 = 0. - Reinhard Zumkeller, Jul 14 2014

a(n) = n + (100^floor(log_100(110*n)) - 1)/11. - Kevin Ryde, Nov 10 2022

Mathematica

Select[Range[0, 1001], EvenQ[Length[IntegerDigits[#]]] &] (* T. D. Noe, Aug 09 2012 *)

Prog

(Haskell)
a001637 n = a001637_list !! (n-1)
a001637_list = filter (even . a055642) [0..]
-- Reinhard Zumkeller, Jul 14 2014
(PARI) is(n)=#Str(n)%2==0 \\ Charles R Greathouse IV, Nov 26 2018
(PARI) a(n) = n + 100^logint(110*n, 100) \ 11; \\ Kevin Ryde, Nov 10 2022
(Python)
def a(n): return n + (100**((len(str(110*n))-1)//2) - 1)//11
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Nov 10 2022 after Kevin Ryde

Crossrefs

Cf. A001633 (complement), A055642.

Sequence in context: A088475 A171891 A328075 * A308407 A102494 A117884

Adjacent sequences: A001634 A001635 A001636 * A001638 A001639 A001640

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved