A117304 Numbers with an even number of digits such that the second half is twice the first half.

12, 24, 36, 48, 1020, 1122, 1224, 1326, 1428, 1530, 1632, 1734, 1836, 1938, 2040, 2142, 2244, 2346, 2448, 2550, 2652, 2754, 2856, 2958, 3060, 3162, 3264, 3366, 3468, 3570, 3672, 3774, 3876, 3978, 4080, 4182, 4284, 4386, 4488, 4590, 4692, 4794, 4896

Offset: 1

Author

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

Keywords

• nonn
• base
• easy

Examples

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

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A019550.

Programs

Mathematica

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 *)

PARI

a(n)={my(k=10^logint(n*9\4,10)); (10*k + 2)*(n + (k-1)*5/9)} \\ Andrew Howroyd, Sep 27 2024

Python

from itertools import count, islice, takewhile
def agen():
    for d in count(2, 2):
        t = (int(str(k) + str(2*k)) for k in count(10**(d//2-1)))
        yield from takewhile(lambda x: x < 10**d, t)
print(list(islice(agen(), 43))) # Michael S. Branicky, Dec 24 2021

Formula

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