A117304 - OEIS

%I #16 Sep 28 2024 02:19:29

%S 12,24,36,48,1020,1122,1224,1326,1428,1530,1632,1734,1836,1938,2040,

%T 2142,2244,2346,2448,2550,2652,2754,2856,2958,3060,3162,3264,3366,

%U 3468,3570,3672,3774,3876,3978,4080,4182,4284,4386,4488,4590,4692,4794,4896

%N Numbers with an even number of digits such that the second half is twice the first half.

%H Michael S. Branicky, <a href="/A117304/b117304.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (10^(k+1) + 2)*(n + (10^k-1)*5/9) where k=floor(log(n*9/4)/log(10)). - _Andrew Howroyd_, Sep 27 2024

%e 1020 is in the sequence because 20 = 2*10.

%t s={};Do[id=IntegerDigits[n];d=Length[id] ;If[EvenQ[d]&&FromDigits[Drop[id,d/2]]==2FromDigits[Drop[id,-d/2]],AppendTo[s,n]],{n,10,4896}];s (* _James C. McMahon_, Sep 27 2024 *)

%o (Python)

%o from itertools import count, islice, takewhile

%o def agen():

%o     for d in count(2, 2):

%o         t = (int(str(k) + str(2*k)) for k in count(10**(d//2-1)))

%o         yield from takewhile(lambda x: x < 10**d, t)

%o print(list(islice(agen(), 43))) # _Michael S. Branicky_, Dec 24 2021

%o (PARI) a(n)={my(k=10^logint(n*9\4,10)); (10*k + 2)*(n + (k-1)*5/9)} \\ _Andrew Howroyd_, Sep 27 2024

%Y Subsequence of A019550.

%K nonn,base,easy

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), Apr 26 2006