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A228011 The largest n-digit number whose last k digits are divisible by k^2 for k = 1..n, otherwise 0. 1
9, 96, 972, 9936, 98000, 990000, 9702000, 90000000, 810000000, 9810000000, 73810000000, 900000000000, 0, 0, 900000000000000, 9900000000000000, 28900000000000000, 0, 0, 90000000000000000000, 0, 0, 0, 900000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(13)=0, a(14)=0 because there are no 13- or 14-digit numbers which satisfy the requirements. The sequence is infinite.

LINKS

Shyam Sunder Gupta, Table of n, a(n) for n = 1..150

EXAMPLE

There are ten one-digit numbers divisible by 1 and largest is 9 so a(1)=9.

For two-digit numbers, the second digit must make it divisible by 2^2, which gives 96 as the largest to satisfy the requirement, so a(2)=96.

MATHEMATICA

a = Table[j, {j, 0, 9}]; r = 2; s2 = 10; t = a; xs = {Last[a]}; While[! a == {}, n = Length[a]; k = 1; b = {}; While[! k > n, z0 = a[[k]]; Do[z = 10^(r - 1)*j + z0; If[Mod[z, r*r] == 0 && r < 25, b = Append[b, z]; t = Append[t, z]], {j, 0, 9}]; k++]; s = Union[t]; s1 = Length[s]; If[r < 25, If[s1 > s2, xs = Append[xs, Last[s]], xs = Append[xs, 0]]]; s2 = s1; a = b; r++]; xs

CROSSREFS

Cf. A079238.

Sequence in context: A228007 A073560 A069055 * A024116 A264208 A070896

Adjacent sequences:  A228008 A228009 A228010 * A228012 A228013 A228014

KEYWORD

nonn,base

AUTHOR

Shyam Sunder Gupta, Aug 08 2013

STATUS

approved

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Last modified October 28 17:39 EDT 2021. Contains 348329 sequences. (Running on oeis4.)