A225608 - OEIS

%I #23 Apr 08 2025 10:02:16

%S 9,98,987,9876,98765,987654,9876545,98765456,987654564,9876545640,

%T 98765456405,987606963096,9876069630960,98760696309604,

%U 987606963096045,9876062430364208,98485872309636009,984450645096105672,9812523240364656789,96685896604836004260

%N The largest n-digit number whose first k digits are divisible by k.

%C There are 25 terms in the sequence; the 25-digit number 3608528850368400786036725 is the largest number to satisfy the requirements.

%H Shyam Sunder Gupta, <a href="/A225608/b225608.txt">Table of n, a(n) for n = 1..25</a>

%H Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_22">On Some Special Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 22, 527-565.

%e There are nine one-digit numbers divisible by 1; the largest is 9 so a(1)=9.

%e For two-digit numbers, the second digit must be even (0,2,4,6,8) to make it divisible by 2, which gives 98 as the largest to satisfy the requirement, so a(2)=98.

%t a=Table[j, {j,9}]; r=2; t={}; While[!a == {}, n=Length[a]; nmax=Last[a]; k=1; b={}; While[!k>n, z0=a[[k]]; Do[z=10*z0+j; If[Mod[z,r]==0, b=Append[b,z]], {j,0,9}]; k++]; AppendTo[t,nmax]; a=b; r++]; t

%K nonn,base,fini,full

%O 1,1

%A _Shyam Sunder Gupta_, Aug 04 2013