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

1,1

Comments

All terms are multiples of 3.

Links

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

Example

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

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 *)

Prog

(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

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).

Sequence in context: A095235 A362404 A316725 * A268540 A030500 A107406

Adjacent sequences: A164775 A164776 A164777 * A164779 A164780 A164781

Keyword

base,nonn

Author

Zak Seidov, Aug 26 2009

Status

approved