Let AOD(i) be the sum of digits of i divided by the number of digits of i, or the Average Of Digits.
N is the smallest integer > 1 such that the AOD(N^k) is the same for k in {1,2,3,4}
M has the same requirements as N, except AOD(M) must be an integer.
L has the same requirements as M, except that L is the smallest such integer with AOD(L) equal to some integer other than AOD(M).
Find:
1. N, AOD(N)
2. M, AOD(M)
3. L, AOD(L)
(In reply to
re(2): Misunderstanding of Part 3 by Larry)
From approximately where I left off, only the integral ones are listed:
709200 3.0 502964640000 356702522688000000 252973429090329600000000
715050 3.0 511296502500 365602564112625000 261424113468732506250000
736200 3.0 541990440000 399013361928000000 293753637051393600000000
750060 3.0 562590003600 421976258100216000 316507512150648012960000
750510 3.0 563265260100 422736210357651000 317267753235520652010000
800640 3.0 641024409600 513229783302144000 410912293703028572160000
806400 3.0 650280960000 524386566144000000 422865326938521600000000
811800 3.0 659019240000 534991819032000000 434306358690177600000000
853200 3.0 727950240000 621087144768000000 529911551916057600000000
901350 3.0 812431822500 732285423210375000 660045466210671506250000
917010 3.0 840907340100 771120439945101000 707125154634057068010000
926100 3.0 857661210000 794280046581000000 735582751138664100000000
996633 6.0 993277336689 989932971896368137 986599867579993065482721
and so L=996633 with an AOD of 6.
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Posted by Charlie
on 2020-08-23 18:40:22 |
re(3): Misunderstanding of Part 3
