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Duplicate each decimal digit of n, so 0 -> 00, ..., 9 -> 99.
8

%I #14 May 07 2022 09:41:46

%S 0,11,22,33,44,55,66,77,88,99,1100,1111,1122,1133,1144,1155,1166,1177,

%T 1188,1199,2200,2211,2222,2233,2244,2255,2266,2277,2288,2299,3300,

%U 3311,3322,3333,3344,3355,3366,3377,3388,3399,4400,4411,4422,4433,4444,4455,4466

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

%C 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).

%C 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.

%H Kevin Ryde, <a href="/A338754/b338754.txt">Table of n, a(n) for n = 0..10000</a>

%F 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.

%F a(n) = A051022(n)*11 for n > 0. - _Kritsada Moomuang_, Oct 20 2019

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

%o (PARI) a(n) = fromdigits(digits(n),100)*11;

%o (Python)

%o def A338754(n): return int(''.join(d*2 for d in str(n))) # _Chai Wah Wu_, May 07 2022

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

%Y Other bases: A001196, A338086.

%K base,nonn

%O 0,2

%A _Kevin Ryde_, Nov 06 2020