A164778 Numbers n with property that average digit of n^2 is s=6.

24, 27, 387, 417, 423, 447, 528, 537, 543, 624, 663, 678, 684, 687, 714, 768, 774, 786, 813, 816, 822, 828, 834, 864, 867, 876, 882, 888, 891, 894, 924, 927, 933, 936, 942, 948, 957, 963, 969, 972, 978, 984, 987, 993, 10386, 11313, 11772, 12114, 12186

Offset: 1

Author

Zak Seidov, Aug 26 2009

Keywords

• base
• nonn

Comments

All terms are multiples of 3.

Examples

			24^2 = 576 and (5 + 7 + 6)/3 = 6
387^2 = 149769 and (1 + 4 + 9 + 7 + 6 + 9)/6 = 6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A164817.

Average of digits of n^2 = s: A164771 (s=1), A164770 (s=2), A164782 (s=3), A164776 (s=4), A164774 (s=5), A164778 (s=6), A164773 (s=7), A164772 (s=8).

Programs

Mathematica

s={};me=6;Do[If[me==Mean[IntegerDigits[n^2]],Print[n];AppendTo[s,n]],{n,3,10^4,3}];s
Select[3*Range[5000],Mean[IntegerDigits[#^2]]==6&] (* Harvey P. Dale, Aug 17 2014 *)

PARI

dsum(n)={my(s=0);while(n>9,s+=n%10;n\=10);s+n};
forstep(n=3,1e6,3,if(dsum(n^2)/#Str(n^2)==6,print1(n","))) \\ Charles R Greathouse IV, Nov 01 2009