OFFSET
0,3
COMMENTS
The smallest m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.
There are infinitely many natural numbers m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 0..19
FORMULA
a(n) > 2/9 * 10^(n/2) for n > 4. - Charles R Greathouse IV, Apr 18 2013
MATHEMATICA
DS[n_] := Total[IntegerDigits[n]]; nn = 10; t = Table[0, {nn}]; n = 0; found = 0; While[n++; r = FromDigits[IntegerDigits[n, 4]]; found < nn, If[DS[r]^2 == DS[r^2] && DS[r] <= nn && t[[DS[r]]] == 0, t[[DS[r]]] = r; found++; Print[r]]]; Join[{0}, t] (* T. D. Noe, Apr 18 2013 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reiner Moewald, Apr 18 2013
EXTENSIONS
a(10) corrected and a(11) added by T. D. Noe, Apr 18 2013
a(12)-a(13) from Donovan Johnson, Apr 19 2013
a(14) from Donovan Johnson, Apr 24 2013
a(15)-a(18) from Hiroaki Yamanouchi, Aug 28 2014
STATUS
approved