A225608 The largest n-digit number whose first k digits are divisible by k.

9, 98, 987, 9876, 98765, 987654, 9876545, 98765456, 987654564, 9876545640, 98765456405, 987606963096, 9876069630960, 98760696309604, 987606963096045, 9876062430364208, 98485872309636009, 984450645096105672, 9812523240364656789, 96685896604836004260

Offset

1,1

Comments

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

Links

Shyam Sunder Gupta, Table of n, a(n) for n = 1..25

Shyam Sunder Gupta, On Some Special Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 22, 527-565.

Example

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

Mathematica

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

Crossrefs

Sequence in context: A147637 A057933 A064617 * A220490 A024115 A066557

Adjacent sequences: A225605 A225606 A225607 * A225609 A225610 A225611

Keyword

nonn,base,fini,full

Author

Shyam Sunder Gupta, Aug 04 2013

Status

approved