A164770 Numbers k with the property that the average digit of k^2 is 2.

145, 152, 179, 190, 251, 3182, 3190, 3199, 3245, 3290, 3335, 3362, 3380, 3470, 3479, 3496, 3550, 3649, 3650, 3749, 3821, 4001, 4010, 4100, 4495, 4496, 4540, 4550, 4585, 4595, 4639, 4649, 4810, 4820, 4910, 4990, 5701, 5710, 5755, 5800, 5900, 6350, 6404

Offset: 1

Author

Zak Seidov, Aug 26 2009

Keywords

• base
• nonn

Comments

There are 6368 such k's < 10^7: see link to 15217.html.

Examples

			145 is a term because 145^2 = 21025 and (2 + 1 + 0 + 2 + 5)/5 = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2500
• Zak Seidov, Average digit of n^2 is 2.
• Zak Seidov, Case with trailing zeros.

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

Select[Range[6500],Mean[IntegerDigits[#^2]]==2&] (* Harvey P. Dale, May 10 2021 *)

PARI

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

Extensions

Edited by Charles R Greathouse IV, Mar 23 2010