A338754 Duplicate each decimal digit of n, so 0 -> 00, ..., 9 -> 99.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 3300, 3311, 3322, 3333, 3344, 3355, 3366, 3377, 3388, 3399, 4400, 4411, 4422, 4433, 4444, 4455, 4466

Offset

0,2

Comments

This is equivalent to changing decimal digits 0,1,..,9 to base 100 digits 0,11,..,99, so the sequence is numbers which can be written in base 100 using only digits 0,11,..,99. Also, numbers whose decimal digit runs are all even lengths (including 0 as no digits at all).

This sequence first differs from A044836 (apart from term 0) at a(100) = 110000 whereas A044836(100) = 10011, because A044836 allows odd length digit runs provided there are more even than odd.

Links

Kevin Ryde, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{i=0..k} 11*d[i]*100^i where the decimal expansion of n is n = Sum_{i=0..k} d[i]*10^i with digits 0 <= d[i] <= 9.

a(n) = A051022(n)*11 for n > 0. - Kritsada Moomuang, Oct 20 2019

Example

For n=5517, digits duplicate to a(n) = 55551177.

Prog

(PARI) a(n) = fromdigits(digits(n), 100)*11;
(Python)
def A338754(n): return int(''.join(d*2 for d in str(n))) # Chai Wah Wu, May 07 2022

Crossrefs

Cf. A051022 (0 above each digit), A044836.

Other bases: A001196, A338086.

Sequence in context: A321536 A110732 A044836 * A033008 A082275 A059544

Adjacent sequences: A338751 A338752 A338753 * A338755 A338756 A338757

Keyword

base,nonn

Author

Kevin Ryde, Nov 06 2020

Status

approved